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.

AI as a Catalyst for Health

computer desk laptop stethoscope
Photo by Negative Space on Pexels.com

Artificial Inteligence, or AI, is no longer the mysterious technological unknown that it once was. In fact, it is now arguably woven into the fabric of our daily lives. Alexa tells us the weather and puts together playlists based on our music choices. Tesco or Ocado personalise our shopping discounts using data from previous purchasing behaviours. Apps predict menstrual cycles and Facebook even serves us ads informed by our browsing habits. 

AI in Health

Through effective automation of processes and problem solving, AI is pushing the boundaries of innovation across practically every industry imaginable. And none more so than healthcare where its use is already relatively widespread. Spanning drug discovery, through automation of diagnosis to supporting patient engagement and adherence, the potential for impact in the sector is exponential. 

With new proven use cases springing up on a regular basis, one area that has shown real promise is screening and diagnostics. A study published in Nature journal earlier this year highlighted the high potential for human error in the identification of breast cancer via mammograms screening. When AI was then introduced as a direct comparator, the technology demonstrated accuracy that surpassed human experts. At a time when the health system is already bursting at the seams and trained professionals are in short supply, integration of AI into the diagnostic journey would seem to make good sense. 

It is also important to note that AI should not be viewed as a replacement for the work carried out by medical professionals. Instead, it should become an additional tool to enhance their capabilities. In the case of medicine, an AI diagnostic model can serve as an additional layer of support and validation for qualified doctors or nurses. This in turn can leave them to focus on other aspects of their roles that an AI machine cannot provide, like quality patient care. 

Improving Outcomes for Patients

collaboration between Moorfields Eye Hospital NHS Foundation Trust and DeepMind Health set out to find new ways to utilise the power of AI to support clinicians in their care for patients. The resulting programme is now able to recommend the correct referral decision for over 50 eye diseases with 94% accuracy, matching world-leading eye experts. Here again, AI continues to demonstrate its potential for the revolution in eye care diagnosis, enabling conditions to be spotted earlier and prioritisation of patients with the most serious conditions. 

At TympaHealth, our focus is on the transformation of ear and hearing care. As with many specialisms, the journey to diagnosis for patients can be long, requiring many consultations with numerous doctors across a variety of specialities. Therefore, it’s our mission to bring ear and hearing care into the community. This includes placing better and faster access to diagnostic and treatment services. AI evidently has an important role in facilitating that. 

There have been limited studies on the use of AI in the context of hearing and ear care. The use of smartphone otoscopes promise to help develop this sector further. Recent studies, including a recent collaboration from the author, use smartphone otoscopes to improve the medical learning environment. In many cases ENT experience is limited in medical school to just one week as a special study block, the advent of artificial intelligence would certainly help in recognising conditions of the ear and streamlining referrals.

Another study, published in Otology and Neurotology last month, showed that machine learning helped to predict post-operative performance of a cochlear implant, as well as identifying the influencing factors. This shows the sector is receptive to this change similar to specialties such as Dermatology and Opthalomology.

Building on these studies, at TympaHealth we have a team to help us embed the technology into our own processes and platforms effectively. In turn this helps us improve diagnostic capabilities and ultimately improve patient outcomes. Much like the Moorfields and DeepMind collaboration for eye health, we aim to use machine learning to assist us in identifying ear conditions. However, that is only the very start. We’re also exploring new ways to harness the power of AI to develop a fully integrated machine learning platform and well as using algorithms as predictors of future ear health deterioration.

A Vision For the Future

In the recent Topol Review which set out a vision for the future of digital health, Eric Topol reinforced the importance of preparing our health and care workforces for a digital future. 

There is clearly a bright future for AI in healthcare, which has proven itself time and time again, especially at a time where technology and digital innovation is beginning to move front and centre in the mission to provide better and faster care. In the UK, our NHS system is already overstretched during usual times, and now with the additional pressures caused by the pandemic, it is imperative that we find new solutions that enable people to access the care they need, whilst relieving the burden on the healthcare professionals. 

Working remotely…

Empty offices seem to be the new norm.

The current situation with #COVID has definitely accelerated a trend that was slowly being embraced. There are some pros and cons.

The chief executive of Barclays, Jes Staley, has suggested that piling 7,000 employees into a tall building “may be a thing of the past”. Large numbers of businesses have reported that productivity has been maintained, or even enhanced, as people work from home. Firms’ accountants will have taken note.

However, the normalisation of remote working will also have an impact on younger workers who, though digitally native, are also more likely to live in cramped circumstances and miss the kind of formative experiences that happen in a physical workplace.