Using maths to grow food ๐ŸŒฑ

With the world population growing by around 80,000,000 people per year ๐ŸŒ, we are facing the challenge to ensure worldwide food security whilst dealing with increasingly degraded soils available for crop production ๐Ÿ‘ฉโ€๐ŸŒพ. In the developed world, synthetic fertilizers are often used to make sure that crops have the nutrients they need to grow. This is extremely damaging to the environment, however, due to the resultant contamination of water supplies๐Ÿ’งand emissions released during production contributing to climate change โ˜€๏ธ โ„๏ธ.

Although soils may have low levels of nutrients, over 78% of our atmosphere is nitrogen ๐Ÿ’จ! Plants are unable to use this themselves; however, special โ€˜Nitrogen-fixingโ€™ bacteria in the soil are able to take this nitrogen and transform it into a form that can be used by plants ๐Ÿ”. A solution to eliminating the need for synthetic fertilizers is, therefore, the formation of these interactions between plants and the special soil microbes ๐Ÿฆ . Currently, legumes such as peas and beans are able to do this, but the most important and widely used cereal crops such as wheat ๐ŸŒพ, rice ๐Ÿš and maize cannot; this is where the maths comes in! ๐ŸŽ‰

Maths can be used to simulate the series of chemical reactions that must take place in plant root cells, on detection of these microbes, in order to utilize the nutrients. In doing this, it has been discovered that specific patterns of calcium concentration are required ๐Ÿ“ˆ. Mathematical equations are then used to model the movement of calcium through the cell, as well as the reactions between calcium and other ‘messenger’ molecules. This involves using computer programmes to simulate changes in calcium patterns between the time when the microbe arrives at the root and when the nutrients are transferred into a form that can be used by plants. If we can understand these processes in legumes, then we can encourage crop plants to do the same!๐ŸŒพ๐ŸŽ‰

Similar models of calcium signal generation are also used in human applications. For example, it is an elevation of calcium concentration in the heart that allows it to beat! Abnormal patterns of calcium in the heart can cause electrical malfunctions and an irregular heartbeat โค๏ธ.

This research is being undertaken by Hayley Mills at the University of Nottingham. ๐Ÿ™Œ๐Ÿป

Using maths to solve crimes ๐Ÿ”Ž๐Ÿšจ (part 2)

From modelling the flow of poisons through the body โ˜ ๏ธ to analysing the trajectory of a bullet ๐Ÿ”ซ to the statistical analysis of DNA found at a crime scene๐Ÿงฌ; maths is used so much in forensics. We have already seen that maths is crucial in analysing any blood that is found at a crime scene๐Ÿฉธ(part 1). We will now look at the importance of maths in the prediction and prevention of crime!

But how can we possibly know when and where a criminal offence is going to take place?! Well, just like the rest of us, criminals can be very predictable. For example, a criminal is unlikely to want to travel a long way to commit a crime but is also not likely to want to do it right on their own doorstep. Using knowledge of crime patterns like this, with lots of data from past crimes, mathematical algorithms can be created to predict where and when crimes are most likely to occur! With this knowledge, police officers can be assigned to locations in the most effective way๐Ÿ‘ฎโ€โ™‚๏ธ๐Ÿ‘ฎ. An example of this is the predictive policing company PredPol, which has resulted in a decrease in crime rate in several areas of the US. Even just knowing that this method is in place could deter any potential criminals and prevent a crime from happening in the first place! So bank robbers watch out…the police are armed with mathematics!

Using maths to solve crimes ๐Ÿ”Ž๐Ÿšจ(part 1)

Ever wondered what they actually do with a taped off crime scene on CSI? ๐Ÿค”They do maths!๐Ÿ˜ From finding a victims time of death to removing the blur from a speed camera image or finding crime hotspots, maths is used so much in forensics. This is the first of several posts that will explain how!

Maths is crucial in analysing any blood that is found at a crime scene in order to find: where the victim was positioned, what weapon was used and if the body has been moved etc. Knowing this info gives us a better understanding of the sequence of events that occurred and therefore helps to catch the correct attacker! ๐Ÿ‘ฎโ€โ™‚๏ธ

Most blood at a crime scene will be the result of a blood spatter from an injury and so will not drop vertically to the ground but at an angle. This means that the blood drops will form ellipses on the ground or surface (not circles). We can use the shape and location of these ellipses to tell us about where the blood came from! By drawing a line through the long axis of each ellipse and extending these lines until they intersect with one another, we find the most probable location of the attack (at the point of intersection). We can then use trigonometry to calculate the most probable height at which this wound was created since the size of the long axis of the ellipse compared to the short axis tells us the angle the blood was spattered from (called the angle of impact). The size of the blood stain tells us about the type of weapon that was used since a smaller stain was likely produced by a higher energy transfer like a gun shot ๐Ÿ”ซ. Maths can also be used in these blood analyses through the modelling of the projectile of the spatter (involving forces like gravity and drag) and the fluid dynamics of the blood.

#usingmathsย #appliedmathematicsย #mathsย #mathschatย #forensicscienceย #bloodanalysisย #crimesย #stemย #stemeducationย #keeplearningย #coolfactsย #scicomm

What do sharks ๐Ÿฆˆ, spider monkeys ๐Ÿ’ , tuna ๐ŸŸ and honey bees ๐Ÿ have in common? They all use maths to find their food!

These 4 extremely different animals (and others) have been found to use the same patterns of movement when searching for their prey. These mathematical patterns, called โ€˜Levy walksโ€™, optimise the animals efficiency in finding their next meal and hence filling their bellies.๐Ÿ‘…

Each step of their movement is chosen randomly and so is not affected by any steps that have already been made (like Dory ๐Ÿ  swimming with her short term memory loss). Some steps are more likely than others, however, (since they are picked from a heavy tailed distribution) and the larger the step distance, the longer it will take before the following step occurs โฑ. This results in lots of short steps as well as the occasional long journey. If a shark canโ€™t find food for example, it might travel a long distance to an area like a coral reef and then take lots of small, random โ€˜stepsโ€™ to look around for the tastiest fish to feast on ๐Ÿฆˆ.

This process can also model stock prices or even social media/general web browsing ๐Ÿ’ป.

#appliedmathematicsย #randomwalkย #brownianmotionย #animalmovementย #foragingย #sharksย #predatorsย #huntingย #mathsย #mathsinlifeย #stemย #scicomm

The maths of modern dating ๐Ÿ’˜

Itโ€™s not for everyone, but we canโ€™t deny that online dating has lead to the start of a significant number of relationships in the past couple of decades. Some of these likely ended after a few months, but for some, online dating allowed them to find the love of their life for which Iโ€™m sure they will be forever grateful ๐Ÿ‘ฉโ€โค๏ธโ€๐Ÿ’‹โ€๐Ÿ‘จ…and you guessed it, itโ€™s all down to maths๐Ÿ‘Œ๐Ÿป๐ŸŽ‰

Dating websites find your matches using a set of rules (an algorithm). For the site OK Cupid ๐Ÿ’˜, this algorithm is based on answers to multiple choice questions. As a user, you answer as many multiple choice questions as you like, as well as giving the answer you would like your potential date to choose and a measure of the importance of that question in your eyes ๐Ÿ‘€ (is it a deal breaker if they leave the toilet seat up? ๐ŸšฝโŒ)

Your potential date is then given a score based on their answers to the same questions, weighted by the importance of those questions in your eyes (you also receive a score weighted by their views on each question importance).

Finally, a match score is decided by multiplying each of your scores together and then taking the nth root where n is the number of questions you answered in common. The higher this match percentage is with someone, the more likely you will show up in their top results ๐Ÿ‘‹๐Ÿป (and for them to be in yours).

Even tinder has a mathematical method to itโ€™s madness in order to determine who you are more likely to see pop up. For this one, it seems that scores are given based on how many people swiped right to you and these are weighted by other factors such as the swipers likelihood to swipe right etc. You are then more likely to see the people that have a score similar to your own.

So could cracking the maths help you find your one true love? ๐Ÿคทโ€โ™€๏ธโค๏ธ

#appliedmathematicsย #findingloveย #mathsย #mathsinlifeย #datingย #tinderย #mathsfactsย #algorithmย #scicomm

Using maths to predict locations of floods and drought๐Ÿ’ง

What we call a hydrological model, is a way of looking at the changes in water resources within the water/hydrological cycle ๐Ÿ” (this is the cycle of water through the earth and its atmosphere by evaporation, condensation and precipitation). Examples of water resources in these models include ice and snow โ„๏ธ, rivers, runoff, streamflow, groundwater and oceans. Maths is used to make estimates about water runoff (excess water across the land), in order to help determine future patterns of flooding or drought.

We divide the surface of the earth into a grid with (x, y) coordinations to define locations across the globe ๐ŸŒŽ๐ŸŒ. Mathematical equations are then used to model how water from one gridcell will flow downhill into another based on the shape of the land. The soil and bedrock are also mathematically modelled (these are assumed to only take in a specific amount rainfall so the extra rainfall becomes surface runoff).

The results from these models can then be used to make estimations about the amount and distribution of water in a certain area. Using this data we can calculate flood and drought risks over time as well as the water availability for human use ๐Ÿฅ›, the environment ๐ŸŒณ and agriculture ๐ŸŒฝ.

This research is being undertaken by Lorna Burnell at the University of Nottingham. ๐Ÿ™Œ๐Ÿป

#appliedmathematicsย #usingmathsย #environmentย #waterย #cycleย #hydrologicalmodellingย #floodriskย #droughtriskย #stemย #communicatingmathsย #scicomm

The maths used to make Woody and his friends – how Pixar make their animations ๐Ÿค—๐Ÿคฉโค๏ธ

We all love a good Pixar film; Toy Story, UP, Monsters Inc, Inside Out are Brave are some of my favourites๐Ÿ˜. But did you know that making these animations needs A LOT of maths? How a character looks, their facial expressions, the way they move, the lighting, colour and textures – they all use maths!!

By starting with just a 4 sided shape and following a simple set of equations to add more lines using the midpoints of these 4 edges (the coordinates of the middle point of each line), the curved surface of Woodyโ€™s face is made to look smooth and realistic. This therefore turns a complicated shape (Woodyโ€™s unique face) into simply lots of lines that a computer can easily deal with. It is how closely these lines are placed that allows each of the characters we love to have different facial features. To animate Woodyโ€™s face, so he can talk for example, the coordinates of just the original 4 points of the shape are translated (moved) to a new position๐Ÿ”นโžก๏ธ๐Ÿ”น, scaled in size or rotated (this uses trigonometry).

In the film Brave, the maths involved in creating just the behaviour of Meridas long curly hair took Pixar over 6 months!๐Ÿ‘ฉโ€๐Ÿฆฑ Letโ€™s give that explanation a miss for now…


Using statistics to improve wheat yields ๐ŸŒพ๐Ÿž

You can find wheat in the ingredient list of so many foods eaten day to day: bread ๐Ÿฅ–, cake ๐Ÿฐ , pizza ๐Ÿ•, pasta ๐Ÿ…(I should know – I am allergic to it! ๐Ÿ˜ญ). As with most crops, the average amount of wheat produced (or the yield) per year increased through the second half of the 1900s with the technical advances in agriculture and more intensive land use. Over the last 20 years however, wheat yields have stayed about the same year on year despite our advancements in knowledge of biotechnology (like genetic modifications to make crops resistant to disease) and climate, during this time. This has caused us to question whether we have reached a maximal level of wheat production?๐Ÿค” Well luckily, we can use maths to test this theory as well as testing possible trade-offs between trying to get a better yield and the potential resultant damage to the environment if we do. ๐ŸŒพ

Extreme Value Theory uses statistical distributions to find (in our case) if there is an upper limit for a wheat yield and if so, what this value is. We can also find out whether other factors such as location or fertilizer use are able to improve this maximum yield by comparing the statistical distributions of each factor level. Knowing this information enables farms ๐Ÿง‘๐Ÿผโ€๐ŸŒพ across the country to find ways of increasing their production to close to this maximum as well as helping with the allocation of funding๐Ÿ’ฐto improve yields across the board.

These methods are more commonly used to estimate the probability that an extreme event occurs, such as large-scale flooding ๐ŸŒŠ, dramatic temperature spikes ๐Ÿ”ฅ or even volcanos erupting! ๐ŸŒ‹

This research is being undertaken by Emily Mitchell at the University of Nottingham. ๐Ÿ™Œ๐Ÿป

#appliedmathematicsย #usingmathsย #mathsinlifeย #foodproductionย #environmentย #wheatย #increasingyieldsย #sustainabilityย #keeplearningย #statisticsย #distributionsย #stemย #scicomm

Using maths to create Virtual Reality ๐Ÿง ๐Ÿ‘€๐Ÿคฉ

I think that we can all agree that Virtual Reality or VR is pretty cool. We all want to escape sometimes, and using VR we can! We can step out of our office or classroom and onto a hawaiian beach ๐Ÿ or the top of Mount Everest ๐Ÿ” . Not only can VR create a fully immersive gaming/entertainment experience, but we see it being used more and more for educational purposes such as simulating historical events ๐Ÿฐ or even in military ๐Ÿ‘ฉ๐Ÿผโ€โœˆ๏ธor medical ๐Ÿง‘๐Ÿฝโ€โš•๏ธtraining. Training for such high risk activities in virtual reality is clearly a massive benefit of this technology considering the risks are reduced to zero!

Virtual reality is exactly what it says on the tin – your brain is tricked into thinking that the virtual/computer simulated environment that you see, is reality! But how does it do this?! –
Well, if you look at an object with one eye closed and then swap to the other eye being closed, the object appears to move slighlty. This is because each of our eyes actually do see the world around us with a slightly different perspective ๐Ÿ‘๐Ÿ‘. It’s our brain ๐Ÿง  that joins these 2 perspectives together and creates the depth in what we are seeing in our 3D world, depending on the difference between the images obtained by each eye. For example, if we look at that object again with each eye closed but this time bring the object closer, the object seems to move even more! We use this to create virtual reality with the help of…(you guessed it) maths! ๐Ÿ™Œ๐Ÿป We know that the average distance between our 2 eyes (specifically the pupils) is about 65mm, we can therefore draw a traingle between each of our eyes and an object and use trigonometry to calculate the (angle) difference between the perspectives of the image for each eye, given the distance of the object. This allows us to create 2 perspectives that are able to trick the brain into thinking that there is depth and, therefore, that we are seeing a 3D reality ๐Ÿ‘€.

In addition to this, sensors measuring the position and angle of your head in a VR headset allows the tracking of your head movements in (x,y,z) coordinates. This enables the images to be adjusted accordingly so that you feel fully transported into the simulated reality.๐Ÿคฉ

You can try virtual reality for yourself at the Deutsches science museum in Munich (see video).


Weird & Wonderful random maths fact ๐Ÿ‘€

Mathematicians at NASA ๐Ÿš€ who simulate the flow of fluids through space rocket engines, have helped to develop a heart pump which can keep patients alive while waiting for a heart transplant โค๏ธ

Just as they model the flow of fuel through the engines of NASA rockets, these mathematicians are able to model blood flow through these pumps (using fluid dynamics!). In doing this they found a way to adapt the design of the pump to reduce the amount of damage to red blood cells as well as the chance of blood clots forming.๐Ÿ‘๐Ÿป

#appliedmathematicsย #usingmathsย #mathsspaceย #rocketย #fluiddynamicsย #flowย #mathematiciansย #savinglivesย #hearttransplantย #stemย #scicomm