Look who I bumped into in Warsaw!

Just thinking about some mathematical problems related to sigma models and string theory wandering round the new physics building in Warsaw…there are some nice views of the city from the 5th floor

warsaw window 1
View from the 5th floor

close up
Pałac Kultury i Nauki

Then just around the corner I met this man…


However, much like Banach, he was not very talkative… my regular coffee guy is a much better conversationalist and knows a thing or two about sigma models.

My brother on Knotweed News report

My brother, Dr G.W. Bruce appeared on the local news in relation to the Japanese knotweed (Fallopia Japonica) problem. Scientists at Swansea University are conducting the largest field trials in Europe to find new ways of killing knotweed.

Fallopia Japonica

Follow the link below for the news report.

Swansea University scientists trial knotweed killers BBC Wales News

UPDATE You can read more about the project, and see a picture of my little younger brother here.

Assume spherical sheep in vacuum…

sheep Scientists have now used GPS to uncover the rules that describe how sheepdogs are able to herd sheep.

Strömbom et al [1] have shown that there are surprisingly few rules here; in fact they suggest just two rules.

  1. The sheepdog learns how to make the sheep come together in a flock.
  2. Whenever the sheep are in a tightly knit group, the dog pushes them forwards.

The sheepdogs make the most of what is know as “selfish herd theory”, that is the tendency of a given sheep to want to be near the centre of the flock when under threat.

There is a Welsh connection here. One of the authors, Dr. A. King is based at Swansea University, which is where I studied for my undergraduate degree.

Now, anyone know any good jokes about Welsh people and sheep? Can’t say that I have herd many…

[1] Strömbom et al, Solving the shepherding problem: heuristics for herding autonomous, interacting agents, J. R. Soc. Interface 11(100) (2014).

The Polish breaking of the Enigma code

The working rebuilt bombe at Bletchley Park Image courtesy of Wikipeda.
Mathematicians from the Polish Cipher Bureau, Marian Rejewski, Jerzy Różycki and Henryk Zygalski broke the German Enigma cipher machine codes in the 1930’s.

Working with engineers from the AVA Radio Manufacturing Company, they built the “Bomba”, which was the first machine to break Enigma codes. By working with a commercially available version of the Enigma machine, they laid down the mathematical foundations that were essential for the British work at Bletchley Park in breaking the German military codes. In particular Alan Turing helped develop the British version of the Bomba and the story from here is well-known.

The efforts of Rejewski, Różycki and Zygalski are far less well-known and were never really appreciated in their lifetimes. There is a small memorial at Bletchley Park in honour of these three.

In August 2014 the Institute of Electrical and Electronics Engineers (IEEE), as part of their Milestones commemorations have honoured Rejewski, Różycki and Zygalski with a plaque outside the Institute of Mathematics of the Polish Academy of sciences. I was lucky enough to be present at the unavailing ceremony which was hosted by IEEE President Prof. J. Roberto B. de Marca. There were several diplomats and representatives from the Polish military. Janina Sylwestrzak, the daughter of Marian Rejewski, was also present and gave a short speech (in Polish of course).

The Rejewski, Różycki and Zygalski memorial stone.

The plaque reads as follows;


You can find out more about the Polish work on breaking the Enigma codes by following the links below.

Milestones:First Breaking of Enigma Code by the Team of Polish Cipher Bureau, 1932-1939 IEEE website.

The Breaking of Enigma by the Polish Mathematicians
, Virtual Bletchley Park.

Poland’s overlooked Enigma codebreakers, BBC News.

Smoking supercapacitors!

scientists from South Korea have converted cigarette butts into a high-performing material that could be used to coat the electrodes of supercapacitors [1].

The material is produces via the heat treatment of used cigarette butts in a nitrogen rich environment.

The article states that the processed cigarette filter material stored a higher amount of electrical energy than commercially available carbon. Also the material stored more energy than the more experimental materials graphene and carbon nanotubes.

If the process can be made economically viable then this process could be used to ecologically recycle cigarette butts.

[1] Minzae Lee, Gil-Pyo Kim, Hyeon Don Song, Soomin Park and Jongheop Yi, Preparation of energy storage material derived from a used cigarette filter for a supercapacitor electrode, 2014 Nanotechnology 25 345601.

Cigarette butts offer energy storage solution IOP News

I am sure this was known about for donkey's years

Researchers at the University of Sussex have published their research on how horses communicate [1]. It seems that they use their swiveling ears to aid in communication.

Talking to someone who is not a scientist, but has lots of experience of working with horses, said that the horse riding community knew this already. However, a scientific study was needed as anecdotal evidence is not enough.

That said, this was known about for donkey’s years*!

*Non-native speakers may find this link useful.

Horses’ mobile ears are ‘communication tool’ BBC News

Jennifer Wathan & Karen McComb, The eyes and ears are visual indicators of attention in domestic horses, Current Biology , Volume 24, Issue 15, 4 August 2014, Pages R677–R679.

Happiness is a long equation

As you can imagine as a mathematician, the bigger and harder the equations the happier I am. Not really, we look for pattens and elegance rather than just difficult equations, though of course difficult equations can be elegant and contain a lot of interesting structure.

Anyway, scientists now have an equation for happiness and here it is

Taken from [1].

Now we just need to apply some calculus to find the maxima (local or global I’m not fussy) and find out just how happy a mathematician can be!

[1] Robb B. Rutledge, Nikolina Skandali, Peter Dayan, and Raymond J. Dolan, A computational and neural model of momentary subjective well-being, PNAS 2014 : 1407535111v1-201407535.

Equation ‘can predict momentary happiness’ BBC News

More experiments with random walks

I have again been playing with some random walks, using the same method as here. This time I used 1000000 iterations and added some colour.

Below are random walks, on the plane (not a lattice) for which step size gets (on average) smaller and smaller with each step. I pick the step size using the Maxwell-Boltzman distribution (with a =1) and a suitable scaling which depends on the iteration parameter. I the add a opacity depending on how many times the points are visited: bright white means a lot, while grey means not many and black never.





Once again, these images are rather for artistic purposes than scientific purposes.