By Carrie Bengston
What would happen if zombies invaded the planet? World War Z tells the story with Brad Pitt and a much bigger film budget than we have.
But it will hearten you to know that a team in Canada has actually crunched the numbers for a zombie apocalypse. They created a mathematical model for zombie infection, suggesting that only quick, aggressive attacks can stave off the doomsday scenario.
The take home message from the maths? Hit ‘em hard and hit ‘em often.
Maths can help us explore all kinds of real and hypothetical scenarios. You might not think it, but maths is vital in understanding the complex and dynamic planet we call home.
This was made clear last week at Mathematics of Planet Earth Year: The Conference, where over 200 people gathered to hear what maths is telling us about our precious planet.
For our young graduate fellows who are test driving a maths research career, the conference was a chance to see the limitless applications of their chosen field. These include an amazing variety of natural and human-organised aspects of planet Earth discussed during the conference.
From understanding climate and weather patterns to identifying pests that threaten our biosecurity using 3D insect imaging, it was evident how important maths is in understanding the many challenges facing Earth today.
Mathematical modelling has even been used to protect people in earthquake-prone areas, promote sustainable dairy farming and watch a virus spread within a plant.
Maths adds a lot of value to our own research too. For instance, our mathematical scientists have contributed to important discoveries about Alzheimer’s disease. Take a look:
2013 is the International year of Mathematics of Planet Earth. Learn more about how maths and stats are helping us understand the challenges of our world.
By Arwen Cross
Love it or hate it, Canberra is our capital city. But it isn’t the only thing named Canberra. Hamish Boland-Rudder has found five other things with the same name, which he described in an article in the Canberra Times last week. It looks like most of them post-date our 100 year old capital, and were named after it.
Canberra is an indigenous placename, but sadly we don’t know what it means or exactly what location the name originally referred to. Some popular suggestions about the meaning of Canberra are ‘meeting place’ or, more racily, ‘the space between a woman’s breasts’, referring to the shapes of Mt Ainslie and Black Mountain. Linguist Harold Koch’s research shows that neither of these explanations is very believable (see page 153, Chapter 5 of Naming and re-naming the Australian landscape). But it’s a rare honour for an Australian capital city to have an indigenous name.
The Canberra distance
One of the things that’s named after the city of Canberra is the Canberra distance, a mathematical function used to sort things according to their similarity.
The Canberra distance was invented by CSIRO scientists Bill Williams and Godfrey Lance in the 1960s. They developed it based on the Manhattan distance, which may have inspired them to name it after their own city, Canberra.
The Canberra distance isn’t a distance in the everyday sense like how far away ANU is from the nearest pub. Mathematicians recognise lots of different types of distances, for example:
- Euclidian distance – the straight line distance between two points. This is similar to our everyday idea of distance.
- Levenshtein distance – the distance between two words measured by how many single-character edits are needed to change one into the other.
- Canberra distance – a measure of similarity and dissimilarity between groups.
So what can you use the Canberra distance for?
It’s often used to sort plants and animals into groups that are more closely or distantly related to each other. Although it can be used outside biology too.
Let’s say you want to separate the sheep from the goats in your large herd. You might need to consider several criteria to make your decision:
- Binary data – has a beard/doesn’t have a beard
- Ordered categorical data – hair very woolly/ hair moderately woolly/ hair not woolly
- Quantitative data – a measurement like weight in kilograms or height in centimetres
The Canberra distance is a way to use all these criteria together to separate individuals according to how similar or dissimilar they are. In our case, we’ll separate the herd according to how sheepy or goaty they are.
If you’ve got a large herd, you’d start by measuring all the criteria for each animal. Then you’d need some statistics, including the Canberra distance, to cluster the data into groups of animals that were similar across several characteristics.
You might find that your herd was made up of three groups of animals: a large cluster of animals with sheepy characteristics, a small cluster with goaty characteristics, and another cluster of animals that is part sheep and part goat.
Going nuts with peanut research
An actual example of the use of the Canberra distance in biological research comes from peanut breeding. Our chief mathematical scientist Bronwyn Harch worked on this project for her PhD. Instead of separating sheep from goats, she was organising peanut plants into groups.
Peanut plants are an important agricultural crop, and plant breeders are always working on new varieties that will grow better in particular climates, be more resistant to disease, or produce a better quality peanut.
To do this they keep collections of seeds from many different peanut varieties. Some wild peanuts might be very resistant to disease but have a poor yield of nuts, while commercial varieties might be disease sensitive but high yielding. Peanut breeders cross varieties to generate new ones and select the offspring with desirable characteristics.
Bronwyn looked at the characteristics of peanuts in the Australian peanut collection and in the world peanut collection in India. Her analysis helped her advise Australian peanut breeders about what characteristics were missing in their collection that they could find in the world collection. Her work also informed scientists going into the Amazon rainforest to collect new peanut plants from the wild about what characteristics to look out for.
The Canberra distance is a useful mathematical tool. But now I’m going to put my feet up and enjoy some of Hamish Boland-Rudder’s other Canberra discoveries – perhaps a glass of Canberra ale.
I would like to thank David Nash and Bob Anderssen for their advice on this article.
By Arwen Cross
Today is world maths day, and students around the world are playing in the World Education Games. If you can solve fifty maths games in an hour, imagine what you could achieve if you applied your maths to finding cancer genes, or timetabling trains. Three vacation scholars in our Mathematics, Informatics and Statistics division have been working on these problems, although they did have 12 weeks instead of an hour to do it.
Shila has been using bioinformatics to look at the genes that are expressed (turned on) in bowel cancer cells compared to normal cells from the same patient. Her statistics should help lab scientists decide which of two methods they should use to measure gene expression in the tissue samples.
Scientists measure RNA levels to see what genes are turned on in the cancer samples, but they have two ways of measuring it. They can use the poly-A method to measure just the genes that make proteins, or they can measure whole RNA. The advantage of whole RNA is that you can find out about regulatory RNA as well as the RNA that gets made into protein. The disadvantage is that the method is newer, so the scientists can’t be sure if it’s suited to this application.
Shila’s statistical analysis showed that the two methods pick up mostly the same differences between cancer and normal tissue. That’s a good thing – it shows both methods are working for genes that make proteins. But her analysis also showed that there are differences between what genes the two methods find. The differences could represent regulatory RNA genes that are involved in the cancer process. Scientists will have to go back to the lab to confirm this.
Shila loves the exploratory aspect of working with large amounts of data, and uncovering patterns in it that you can’t pick out without statistics to help you. She’s off to do a PhD next year.
Josh and Joe have been using maths for solving problems related to trains, including timetables and infrastructure planning.
Joe worked on the problem of how to timetable trains most efficiently when mining trains have to travel on sections of single track. If there are only a few places to overtake, the number of trips is limited because only one train can travel in one direction at a time. That makes optimal timetabling really important. Since the timetabling problem is too complex for solver software products, Joe worked with other methods to get the best solution.
Joe travelled from Brisbane to Melbourne for his vacation scholarship because he was so keen to do a project in operations research. He chose this area because it combines all the best things he likes about maths, programming and problem solving. Joe will be doing an honours year in his maths and computational science course this year.
Josh worked on a tablet interface for our IFAP software which helps planners design infrastructure. It provides information about questions like whether it would be more useful to build a new train line to a mine, or to upgrade another line that services mines which are increasing their output. Governments use this type of tool so they can plan infrastructure funding to get the best outcome for the money spent. Josh worked on developing an Android application so that IFAP can be used on mobile devices.
Josh enjoyed applying his uni knowledge to a new area, and found it useful to link his experience of different technologies and find out how they work together. He’ll be continuing his undergraduate degree this year.
From cancer genes to train timetables, maths can help solve a lot of problems. Students worldwide are participating in World Maths Day today. Maybe some of them will be vacation scholars too in a couple of years.
By Bruce Tabor
On 15 February, the sky over Russia was lit up by a great ball of fire – the Chelyabinsk meteor. NASA’s infrasound data can tell us a lot about it. But amazingly, so can amateur sleuths using YouTube, Google Earth, and some trigonometry.
The Chelyabinsk meteor entered the atmosphere, and exploded at high altitude near the Russian city of Chelyabinsk at 9:20 am local time Friday 15 February. Normally we rely on national space-science agencies to reconstruct these events but with some data from the web and some high school physics, you too could try your hand.
Stefan Geens of Ogle Earth was inspired to use maths to find out about the meteor using footage from car dash-board and building security cameras in Russia, which have proliferated as a way of fighting crime.
He made some assumptions about straight lines and constant speeds, and got some videos of the meteor over Revolution Square, Chelyabinsk. Then he used the distance between light posts to do some trigonometry.
To use this method you need some information. The explosion occurred at an elevation of 40 degrees almost due south of Chelyabinsk’s Revolution Square. The meteor was travelling a little south of due west.
You can get more information about distances using the gap between the flash of light and the sound of the explosion in the security camera footage. Time-stamped surveillance suggests a delay about 2.5 minutes until the shock wave reached the city. Assuming an average speed of sound of say 300 metres per second, you can calculate a distance.
Using two sides and one angle, you’re ready to do some trigonometry. The meteor exploded 45 km away at a height of about 35,000 metres. That’s three times higher than commercial airlines fly.
Most meteors start out their lives as asteroids, but when these rocks enter the atmosphere at high speed they change their name to meteor. Asteroids move through space on their own paths, but if they pass very close to us they can be effected by Earth’s gravity. Some of them enter our atmosphere and become meteors.
It’s friction with the atmosphere that makes them burn up as their kinetic energy gets converted to other forms like heat, light and sound (great balls of fire!).
So how much kinetic energy did the Chelyabinsk meteor have? NASA used infrasound data to find out. They estimate that the meteor had a diameter of 17 metres, a mass of 10 000 tonnes and entered the Earth’s atmosphere at nearly 18 kilometres per second.
Kinetic energy increases with the square of speed, so the astronomical velocity of the meteor meant that it had a lot of energy. And within a fraction of a second this energy of about 2 petajoules – that is 2 with 15 zeros – was converted into heat, light, and a blast wave.
There was 50 times more energy released by the Chelyabinsk meteor than would be released by an explosion of the same mass of TNT. That’s 30 times the Hiroshima blast and the largest energy release from a meteor since 1908 (when the Tunguska event released the equivalent of 10-15 megatons of TNT). Fortunately this blast occurred high in the atmosphere, which is why the damage on the ground was mostly limited to shattered windows.
All I can say is – goodness, gracious, great balls of fire!
This article celebrates 2013, the year of Maths of Planet Earth. The article was written by Bruce Tabor and edited by Arwen Cross. Thanks to John Sarkissian for proofreading for us.
By Carrie Bengston
The 85th Academy Awards will be televised tonight and high-tech visual effects play a big part in the movies nominated for an Oscar. Animation or computer generated imagery is responsible for visual effects in Life of Pi, The Hobbit and other movies. Modelling water, smoke and fire are niche areas of computer generated imagery. This year a ‘tech Oscar’ was awarded to Swiss university ETH Zurich and Disney studios for animating smoke and explosions.
The winning researchers developed computer simulation techniques to make realistic animated explosions and smoke for movies. The ‘Technical Achievement Award’ is an Oscar that recognises the nerdy know-how behind what we see on screen and puts science on the red carpet. Lab coats with diamantes anyone?
The award is one of nine scientific and technical achievements honoured this year by the US Academy of Motion Picture Arts and Sciences.
Here at CSIRO, our fluids modelling team have also dipped their toes in the virtual water of special effects computer modelling. The Melbourne team developed a plug-in for Maya, a popular animation software used by movie makers worldwide. Their computer models use real science to create super realistic fluid special effects. The plugin has been trialled by several studios. While major studios aren’t currently using it, it’s proved a fantastic tool for modelling natural disasters in the real world.
Our fluids modelling software builds in the maths that governs physical processes like bubbles forming in beer, water rushing down a staircase in the sinking Titanic and a martini glass filling. This means effects are built ground-up from real science rather than just creating an effect that looks cosmetically similar. It also uses less computer power, which makes it faster and cheaper – an important consideration for budget-conscious movie studios.
CSIRO Team Leader Mahesh Prakash says that simulating water and smoke are both very challenging.
“Water and smoke effects in animation are easy to get wrong and movie-goers can tell straight away if something looks fake. Our congratulations to the ETH Zurich-Disney team for their tech award. It shows the contribution science can make to the multi-billion dollar entertainment industry,” he said.
Mahesh said that CSIRO and ETH Zurich-Disney are using two quite different mathematical approaches in their models but both are valid. For the tech-heads, his team use smooth particle hydrodynamics while ETH use wavelets.
“Our methods can be used for smoke effects as well,” he said.
In a classic example of applying of life imitating art, research done by his team for movie special effects research is now being used to model real natural disasters like floods or tsunamis or storm surges. The models are overlaid on terrain maps of real locations.
For example, ‘texturing’ in a computer model creates realistic surfaces on landscapes such as trees on a hill, wind-rippled desert dunes, or buildings near a harbour. This is useful for both movie special effects and modelling disasters, such as seeing what would happen if a hypothetical seven metre tsunami wave hit Fremantle in WA.
And a game engine used for exploring different camera angles, zooms and pans for movies can be used by disaster managers to analyse extreme events to help plan for the future.
So – lab coats with bling on the Oscars red carpet? We think so.
By Sarah Wood
This week is the 100th anniversary of Titanic’s maiden voyage and her sinking.
While there will be endless documentaries on our television, new books (one even written by one of our own CSIRO staff member and best selling Titanic author Daniel Klistorner) and the release of James Cameron’s ‘Titanic’ in 3D, something about Titanic just captures people.
It had me thinking about one of our most successful CSIRO YouTube videos You’re on the Titanic when it sinks
At one point this video had over 900,000 views before we moved it over to our official CSIRO channel in 2009. It now has over 486,000 giving it a total of around 1.3 million views, which when you think about it is pretty impressive really.
While the video might seem pretty primitive compared to James Cameron’s Hollywood blockbuster (hey we weren’t working with the same budget) back in 2005 it demonstrated how we’d taken science out of the lab and placed it in the hands of animators.
The software developed by CSIRO to model the water and the martini, uses chaos theory and other mathematical algorithms in a technique called Smoothed Particle Hydrodynamics (SPH). This method models millions of tiny water particles in a fluid – similar to the way 100s and 1000s seem to flow if you poured them out of a jar.
CSIRO scientists were using the SPH technique to model the fluid and particle processes in big industrial machines when they realised that the software they created could help animators realistically represent fluids in movies.
When animators create water and waves for big budget films like Titanic or Pirates of the Caribbean, the process can take months and hours of meticulous tweaking of wire meshes -the structure over which animators tell the water to flow.
But CSIRO’s methods were much faster and extremely accurate enabling animators to easily and economically create special effects such as bubbles, eddies, spray, smoke and even fire!
So CSIRO created a plug-in for MAYA, the software of choice for high-end 3D animators to allow them access to this technology.
To create this Titanic video our fluid modelling scientists worked with production company Complete Post to test out the plug-in. They also had other leading film companies test the software such Animal Logic and Weta Digital in New Zealand who worked on animations for Avatar, Lord of the Rings, Planet of the Apes and TinTin.
While we’ve moved on from Titanic, we’re now modelling other disasters such as tsunamis, dam breaks, floods, mudslides and storm surges and our methods have certainly come a long way!
“In recent years, the huge increase in computer power and speed, along with advances in algorithm development, have allowed mathematical modellers like us to make big strides in our research,” says Mahesh Prakash of CSIRO’s computational modelling team.
Faster and more powerful supercomputers are making it possible to model millions even billions of particles making our videos look far more cinematic! We also have a full time graphics artist on staff that makes our fluid modelling videos look amazing and we’ve even gone 3D to display our videos in all their glory!
If you’ll be in Sydney for the CeBIT IT trade fair from 22-24 May come see our latest videos in 3D on the CSIRO stand.
Check out some of our more recent videos here:
Modelling Dam breaks and Tsunamis and other geophysical events
Indeed, today is Pi Day – 3.14 if you write the date that way. It’s a day to celebrate the mathematical constant that is 3.1415926… I could go on. I mean really go on. Because Pi has no end.
In fact, on Pi Day 2004, a guy named Daniel Tammet recited Pi to 22,514 decimal places. So much for thinking we’d struck upon genius a few years ago at CSIRO when one of our Newcastle scientists managed to get to 241 decimal places before slipping up. She was eating a pie at the time, so we blamed it.
You’ve probably got fond memories of Pi and the efforts you went to trying to remember equations like πr2 and 2πr for your maths exams. Stupid circles, you uttered. Well, today’s the day to replace those haunted memories with celebration.
According to Wikipedia, there are many ways to celebrate Pi Day: “Some of them include eating pie and discussing the relevance of π.” Sounds like a hoot.
So, in the interest of celebration, let me begin my steak and kidney delight (with a generous squirt of tomato sauce) and tell you what I found out when I tried to ‘discuss the relevance of Pi’ with a few of my colleagues from CSIRO’s Mathematics, Informatics and Statistics gang:
“What would we do without Pi? Probably spend most of our time going in circles, because we wouldn’t know when they finish.”
“I still remember the feeling that came over me when my lecturer proved that Pi equalled Pi. It was quite profound.”
“I don’t celebrate Pi Day on 3.14 – I celebrate Pi day on 22/7. The date’s in the right order for Australia, and it’s also a slightly better mathematical approximation of Pi. On 22/7, I team up with a local Canberra maths guy to give a presentation on the wonders of Pi. We usually do it down at the pub, so we can enjoy pies and pints afterwards.”
“If mathematics is the music with which the symphony of the universe is written, then the eternity of Pi is the measure of its beauty.”
Poetic. A pie to each of them. It’ll certainly be an energy (albeit calorie-laden) boost for the more serious work they’re doing… find out more at http://www.csiro.au/org/CMIS