Month: November 2022

You probably clicked on this blog because you’re either very excited or terrified at the idea of encountering a robot at your next visit to the doctor’s office. Let me first reassure – or disappoint you – we’re not talking about robots here. Instead, this blog post is about artificial intelligence (AI)-assisted cancer detection. While this may at first sound less cool than robots, it could actually save many lives by detecting cancer more accurately and earlier than doctors currently can.

The most common cancer today and the second deadliest one among women is breast cancer. A recent study by a team around Christian Leibig found that when AI and a radiologist – doctors who analyse breast cancer screening images – work together, they can identify breast cancer more accurately than radiologists by themselves.

So how does this system work? Firstly, let’s talk about AI. The kind of AI used here is based on a technology called computer vision, where AI learns to recognize patterns from a huge number of breast screening images. When it is shown a new image, it can thus identify if the patterns for cancer (or certain types thereof) are present. Moreover, the AI algorithm studied by Leibig and his team also tells you how confident it is in its findings. When working together with a radiologist, the images which the AI assistant is not sure about will then be looked at by the doctor. Only those which the AI assistant is very certain about are automatically forwarded to the next step in the hospital’s procedure. For example, the AI’s findings may be passed on to the ‘consensus conference’, where several doctors decide whether to give a cancer diagnosis.

Leibig and his team compared how well AI-assisted radiologists did when detecting cancer on over a million breast cancer screening images, to how well radiologists and AI each did on their own. The scientists found that the AI-assisted radiologists scored the highest, both at detecting when cancer was present, as well as when it wasn’t. This means that the AI-assisted radiologist is more likely to be correct in telling you that you have cancer, and also that it is more likely to be right when it tells you that you don’t, compared to radiologists working alone.

Hence, when AI and doctors work together in identifying cancer, this can lead to a more accurate cancer diagnosis. Also, in this collaboration, humans always retain the final say, making this a rather safe way of using AI. What’s more, being able to focus on fewer, difficult images enables the radiologist to play to their strengths and do less – but nevertheless valuable – work. A reduced workload not only improves their quality of life, but also enables them to make more accurate diagnoses, since they are not exhausted from having looked at mountains of similar screening images all day. All this is ultimately for the best of patient and may save many lives: If an AI-assisted radiologist can find a patient’s cancer that would have otherwise gone undetected, or if the cancer can be found earlier than otherwise, the patient has better chances of healing thanks to AI.

So hopefully, after reading this, those excited about meeting a robot at the doctor’s office will be slightly less disappointed, knowing that AI could soon help their doctor when analysing cancer screening images. And those worried about AI technology entering their lives will hopefully also feel better, knowing that this form of AI technology is controlled and assisted by humans, and that it could actually save your life one day.

 

Source:

Leibig, C. et al. (2022) ‘Combining the strengths of radiologists and AI for breast cancer screening: a retrospective analysis’, The Lancet Digital Health, 4(7), doi: 10.1016/S2589-7500(22)00070-X

Author:

Lene Bierstedt

In 1689, famous swiss professor Jakob Bernoulli paid attention to a quite specific mathematical problem, which is sum of infinite reverse squares, today it is known as Basel problem. Although formulation itself sounds a bit fancy for non-mathematician, it is just summation of series where 1 is divided by number squared:

Not too complicated if you managed to pass school math, but in the 17th century without calculators and computers, and limited knowledge about series it could take a while to find out the solution, especially considering that numbers go on to infinity…

 

46 years later, in 1735 swiss mathematician Leonard Euler was able to find out that infinite sum of reverse squares equals 𝛑2/6. Wow! Why would 𝛑 appear somewhere else than in circle area? Although Euler himself used very complicated math, proving this identity can be understood even by 9th graders, and yes, it involves circles. 

 

So why would 𝛑 appear in such non-related to geometry problem? Let’s find out!

 

Inverse squares appear in physics, in fact, if you imagine a light source at a distance one unit from you, the brightness received by your eye would be 1, but if it is at a distance two units away, you would see only one fourth of the original brightness. Hence, at distance three you see only one ninth of original brightness, this comes from properties of light and other physical quantities such as heat, sound, radio waves and etc. We can already see what are next steps… In the theoretical approach Basel problem can be represented within physical objects. 

 

But how can we manipulate our light sources to understand the math behind? 

It would be quite easy, in the picture above imagine yourself standing at point C, and the light source would be on point X. Due to properties of Pythagorean theorem (its inverse to be precise), the brightness received by your eyes from light source at point X would be the same if there were two same light sources at points A and B. Therefore we can “exchange” one light source to two other similar ones which lie on the apex of the right triangle. 

To refresh school memory, I remind you that if one of triangle’s side is circle’s diameter, and the third apex is on the side of circumference, than it would always be right triangle with perfect 90 degree angle. 

 

Can you already see where it is going? =) 

If you imagine yourself standing on point P and your light source is on point Q, where PQ is the diameter of a circle, it would be the same physical picture in terms of brightness received by your eye if there was a circle twice as big and there were two light sources on sides of a bigger circle. And we can keep adding light sources on the sides of a circle which is twice bigger until we end up standing on the edge of a circle of infinite circumference with the same brightness received by our eyes! 

 

Now, back to school geometry, consider that length of a circumference is 2𝛑r, and all over the circle on same evenly spaced distance there are our light sources which appear with same brightness to our eyes, but each would be in the inverse distance squared. Simple algebraic manipulations lead to the final cut: adding inverse squares up to infinity comes up to be… 𝛑2/6! Boom!

 

Knowing the properties of physical quantities, light in our case, and simple Euclidean geometry can help us to prove the Basel problem without too complicated formulas. 

 

In fact, there are tonnes of other modern methods to prove Basel problem, for example some other way would look something like this:

Too bad those guys did not pay attention in their geometry lessons in 8th grade!

Based on: No. 524 (July 2008), pp. 313-316 Johan Wästlund, “Summing inverse squares by euclidean geometry” http://www.math.chalmers.se/~wastlund/Cosmic.pdf

Filipp Volodin

With the fall of Roman Western Empire, techniques for concrete construction were lost. People admired the ancient buildings for hundres of years, hoping that one day civilization will regain its lost knowledge one day. In a similar way, a few years ago audio DIY communities were swept by the newest rediscovery – giant free-hanging panels to which an exciter is attached, creating vibrations that practically turn the panel into a giant source of sound. Panel speakers have been around at least since the 60’s, but now the technology is advanced enough that any teen with a hammer and a nail can build one themselves. But should they?

What is it like to listen to such a speaker? Some people say it’s like listening to a live school orchestra performing film music: you can hear it all over the place but every now and then some messes up their part. Why? Panel speakers have more on their plate than normal speakers. Because of their complexity, they vibrate in not 2, not 3, but 4 distinct types of waves! You might ask: wait, weren’t there supposed to be only longitudinal (sound-like) and tranverse (water-like) waves in physics? Well, this is what a teen with a hammer and a nail believes, and this is what makes him and his panels wrong.

Unmoving panel cross-section

Panel vibrating a quasi-longitudinal wave

Panel speakers also exhibit other types of waves, for instance the quasi-longitudinal wave. This means that the panel stretches and compresses (just like air molecules), but if you look only at the surface, the wave looks tranverse. Another type of wave is the bending wave, which looks either like an earthquake or a falling stack of books depending on how you look at it. It is a combination of tranverse and logitudinal waves.

Panel vibrating a bending wave

Bending wave is the real hair in the soup of panel speaker enthusiasts, because it is frequency dependent. This means that however we design a panel speaker, it will produce a different vibration and hence a different sound for specific tones in a piece of music – essentially distorting your favourite jams.

Another problem arises when with the resonance: panel speakers love to resonate in different frequencies with transverse waves. You might notice this when you get to listen to your big bass speakers in a living room on a Sunday morning and hear your glasses clanking in a cupboard on the drop. This is because whenever a frequency is played, a corresponding wave exists, that might just happen to be the length of a piece of glassware. In panel speakers specifically, a resonance might occur because a wave is established between an exciter and an edge of the panel. Because most panel speakers are rectangles, the resonance occurs for some frequencies and not for others, creating what you might call a false tune. When I used to be a teen with a nail and a hammer, I once tried to get away with that problem making an egg-shapped speaker: if you put an exciter on the bottom of such a panel, theoretically almost all waves resonate equally, so it seems logical that all frequencies should have the same loudness.

The bending waves are notoriously hard to please though: the resonance of bending waves depends on the frequency in a non-linear way! This means that there is more resonance for some frequencies than others if the radius of the egg increases linearly, which is necessary for an equal response for transverse waves. A solution for one type of a wave creates problem for a different type. This is why panel speakers are difficult to create on par with traditional speakers, and why the technology is ditched every now and then. Perhaps better computational models will bring improved giant speakers in the future. If you could get an AI to test different shapes of speakers, for instance, it could analyze how the vibration interact with each other to create sound and find a design that has the least mean difference between the loudness of all frequencies. For now, however, we can enjoy just this: a crazed orchestra of different waves dancing on the biggest speakers you’ve ever seen.

Angus, J. Distributed Mode Loudspeaker Resonance Structures. Journal of the Audio Engineering Society 5217, (2000). http://www.aes.org/e-lib/browse.cfm?elib=9121

 

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