Quantum magic squares

Quantum magic squares

In a new paper in the Journal of Mathematical Physics, Tim Netzer and Tom Drescher from the Department of Mathematics and Gemma De las Cuevas from the Department of Theoretical Physics have introduced the notion of the quantum magic square, which is a magic square but instead of numbers one puts in matrices.

This is a non-commutative, and thus quantum, generalization of a magic square. The authors show that quantum magic squares cannot be as easily characterized as their “classical” cousins. More precisely, quantum magic squares are not convex combinations of quantum permutation matrices. “They are richer and more complicated to understand,” explains Tom Drescher. “This is the general theme when generalizations to the non-commutative case are studied. Check out the paper!

Quantum magic squares: Dilations and their limitations: Journal of Mathematical Physics: Vol 61, No 11
— Read on aip.scitation.org/doi/10.1063/5.0022344

2020 Nobel Prize in Physics – Black holes

I had intended to post this much ealier on, and certainly closer to the actual announcement of the Nobel Prizes in early October. It has however been a very busy period. Better late than never, right?

I was very pleased to see that the winners of the 2020 Nobel Prize in Physics were a group that combined the observational with the theoretical. Sir Roger Penrose, Reinhard Genzel, and Andrea Ghez are the recipients of the 2020 Nobel Prize in Physics. Penrose receives half the 10 million Swedish krona while Ghez and Genzel will share the other half.

Penrose’s work has taken the concept of black holes from the realm of speculation to a sound theoretical idea underpinning modern astrophysics. With the use of topology and general relativity, Penrose has provided us with an explanation to the collapse of matter due to gravity leading to the singularity at the centre of a black hole.

A few decades after the 1960’s work from Penrose we have Genzel and Ghez whose independent work using adaptive optics and speckle imaging enabled them to analyse the motion of stars tightly orbiting Sagittarius A*. Their work led to the conclusion that the only explanation for the radio source at the centre of the Milky Way’s was a black hole.

Ghez is the fourth woman to be named a Nobel physics laureate, after Donna Strickland (2018), Maria Goeppert Mayer (1963), and Marie Curie (1903).

From an Oddity to an Observation

In 1916 Karl Schwarzwild described a solution to Einstein’s field equation for the curved spacetime around a mass of radius r. Some terms in the solution either diverged or vanished for r=\frac{2GM}{c} or r=0. A couple of decades later, Oppenheimer and his student Hartland Snyder realised that the former value corresponded to the radius within which light, under the influence of gravity, would no longer be able to reach outside observers – the so called event horizon. Their work would need more than mathematical assumptions to be accepted.

By 1964 Penrose came up with topological picture of the gravitational collapse described and crucially doing so without the assumptions made by Oppenheimer and Snyder. His work required instead the idea of a trapped surface. In other words a 2D surface in which all light orthogonal to it converges. Penrose’s work showed that inside the event horizon, the radial direction becomes time-like. It is impossible to reverse out of the black hole and the implication is that all matter ends up at the singularity. Penrose’s research established black holes as plausible explanation for objets such s quasars and other active galactic nuclei.

Closer to Home

Although our own galaxy is by no means spewing energy like your average quasar, it still emits X-rays and other radio signals. Could it be that there is a black hole-like object at the heart of the Milky Way? This was a question that Genzel and Ghez would come to answer in time.

With the use of infrared (IR) spectroscopy, studies of gas clouds near the galactic centre showed rising velocities with decreasing distances to the centre, suggesting the presence of a massive, compact source of gravitation. These studies in the 1980s were not definitive but provided a tantalising possibility.

In the mid 1990s, both Genzel and Ghez set out to obtain better evidence with the help of large telescopes operating in the near-IR to detect photons escaping the galactic center. Genzel and colleagues began observing from Chile, whereas Ghez and her team from Hawaii.

Their independent development of speckle imaging, a technique that corrects for the distortions caused by Earth’s atmosphere enabled them to make the crucial observations. The technique improves the images by stacking a series of exposures, bringing the smeared light of individual stars into alignment. In 1997, both groups published their measurements stars movements strongly favouring the black hole explanation.

Further to that work, the use of adaptive optics by both laureates not only improved the resolutions obtained, but also provided the possibility of carrying out spectroscopic analyses which enabled them to get velocities in 3D and therefore obtain precise orbits.

The “star” object in this saga is the so-called S0-2 (Ghez’s group) or S2 (Genzel’s group) star. It approaches within about 17 light-hours of Sagittarius A* every 16 years in a highly elliptical orbit.

Congratulations to Ghez and Genzel, and Penrose.

Let there be light: Florence Nightingale

This year, 2020, the word Nightingale has acquired new connotations. It is no longer just a word to refer to a passerine bird with beautiful and powerful birdsong, it is the name that NHS England has given to the temporary hospitals set up for the COVID-19 pandemic. In normal circumstances it is indeed a very good name to use for a hospital, but given the circumstances, it becomes more poignant. It is even more so considering the fact that this year, 2020, is the bicentenary go Florence Nightingale’s birth.

Florence Nightingale was born on 12th May, 1820 in Florence, Italy (hence the name!) and became a social reformer, statistician, and the founder of modern nursing. She became the first woman to be elected to be a Fellow of the Royal Society in 1874.

With the power of data, Nightingale was able to save lives and change policy. Her analysis of data from the Crimean War was compelling and persuasive in its simplicity. It allowed her and her team to pay attention to time – tracking admissions to hospital and crucially deaths – on a month by month basis. We must remember that the power of statistical tests as we know today were not established tools and the work horse of statistics, regression, was decades in the future. The data analysis presented in columns and rows as supported by powerful graphics that many of us admire today.

In 2014 had an opportunity to admire her Nightingale Roses, or to use its formal name polar area charts, in the exhibition Science is Beautiful at the British Library.

Florence Nightingale’s “rose diagram”, showing the Causes of Mortality in the Army in the East, 1858. Photograph: /British Library

These and other charts were used in the report that she later published in 1858 under the title “Notes in Matters Affecting the Health, Efficiency, and Hospital Administration of the British Army”. The report included charts of deaths by barometric pressure and temperature, showing that deaths were higher in hotter months compared to cooler ones. In polar charts shown above Nightingale presents the decrease in death rates that have been achieved. Let’s read it from her own hand; here is the note the accompanying the chart above:

The areas of the blue, red & black wedges are each measured from the centre as the common vortex.

The blue wedges measured from the centre of the circle represent area for area the deaths from Preventible or Mitigable Zymotic diseases, the red wedged measured from the centre the deaths from wounds, & the black wedged measured from the centre the deaths from all other causes.

The black line across the read triangle in Nov. 1854 marks the boundary of the deaths from all other caused during the month.

In October 1854, & April 1855, the black area coincides with the red, in January & February 1855, the blue area coincides with the black.

The entire areas may be compared bu following the blue, the read & the black lines enclosing them.

Nightingale recognised that soldiers were dying from other causes: malnutrition, poor sanitation, and lack of activity. Her aim was to improve the conditions of wounded soldiers and improve their chances of survival. This was evidence that later helped put focus on the importance of patient welfare.

Once the war was over, Florence Nightingale returned home but her quest did not finish there. She continued her work to improve conditions in hospitals. She became a star in her own time and with time the legend of “The Lady with Lamp” solidified in the national and international consciousness. You may have heard of there in the 1857 poem by Henry Wadsworth Longfellow called “Santa Filomena”:

Lo! in that house of misery
A lady with a lamp I see
Pass through the glimmering gloom,
And flit from room to room

Today, Nightigale’s lamp continues bringing hope to her patients. Not just for those working and being treated in the NHS Nightingale hospitals, but also to to all of us through the metaphorical light of rational optimism. Let there be light.

Science Communication – Technical Writing and Presentation Advice

The two videos below were made a few years ago to support a Science Communication and Group Project module at the School of Physics Astronomy and Mathematics at the University of Hertfordshire. The work was supported by the Institute of Physics and the HE STEM programme. I also got support from the Institute of Mathematics and its Applications. The tools are probably a bit dated now, but I hope the principles still help some students trying to get their work seen.

The students were encouraged to share and communicate the results of their projects via a video and they were supported by tutorials on how to do screencasts.

Students were also encouraged to prepare technical documentation and the videos for using LaTeX and structuring their documents with LaTeXwere very useful.

Technical Writing

This presentation addresses some issues we should take into account when writing for technical purposes.

Presentation Advice

In this tutorial we will address some of points that can help you make a better presentation either for a live talk or for recording.

Screencasting with Macs and PCs

The videos below were made a few years ago to support a Science Communication and Group Project module at the School of Physics Astronomy and Mathematics at the University of Hertfordshire. The work was supported by the Institute of Physics and the HE STEM programme. I also got support from the Institute of Mathematics and its Applications. The tools are probably a bit dated now, but I hope the principles still help some students trying to get their work seen.

Students were asked to prepare a short video to present the results of their project and share it with the world. To support them, the videos below were prepared.

Students were also encouraged to prepare technical documentation and the videos for using LaTeX and structuring their documents with LaTeX were very useful.

Screencasting with a Mac

In this video we will see some tools to capture video from your screen using a Mac. The tools are Quicktime Player, MPEG Streamclip and iMovie.

Screencasting with a PC

In this video we will see some tools to capture video from your screen using a PC. The tools are CamStudio and Freemake Video Converter.

Uploading a Video to Vimeo

In this tutorial we will see how to set up an account in Vimeo and how to upload your screencast. Also you will be able to send a link to your video to you friends and other people.

Structured Documents in LaTeX

This is a video I made a few years ago to encourage my students to use better tools to write dissertations, thesis and reports that include the use of mathematics. The principles stand, although the tools may have moved on since then. I am reposting them as requested by a colleague of mine, Dr Catarina Carvalho, who I hope will still find this useful.

In this video we continue explaining how to use LaTeX. Here we will see how to use a master document in order to build a thesis or dissertation.
We assume that you have already had a look at the tutorial entitled: LaTeX for writing mathematics – An introduction

Structured Documents in LaTeX

LaTeX for writing mathematics – An introduction

This is a video I made a few years ago to encourage my students to use better tools to write dissertations, thesis and reports that include the use of mathematics. The principles stand, although the tools may have moved on since then. I am reposting them as requested by a colleague of mine, Dr Catarina Carvalho, who I hope will still find this useful.

In this video we explore the LaTeX document preparation system. We start with a explaining an example document. We have made use of TeXmaker as an editor given its flexibility and the fact that it is available for different platforms.

LaTeX for writing mathematics – An introduction

Natural Language Processing – Talk

Last October I had the great opportunity to come and give a talk at the Facultad de Ciencias Políticas, UAEM, México. The main audience were students of the qualitative analysis methods course, but there were people also from informatics and systems engineering.

It was an opportunity to showcase some of the advances that natural language processing offers to social scientists interested in analysing discourse, from politics through to social interactions.

The talk covered a introduction and brief history of the field. We went through the different stages of the analysis, from reading the data, obtaining tokens and labelling their part of speech (POS) and then looking at syntactic and semantic analysis.

We finished the session with a couple of demos. One looking at speeches of Clinton and Trump during their presidential campaigns; the other one was a simple analysis of a novel in Spanish.

Thanks for the invite.