Fellow colleague Paolo Bonfini joins Angelo to discuss how computer science has helped us better understand the evolution of galaxies. Paolo and Angelo dive deep into how galaxies are formed and evolve over time.
The episode touches on the wondrous journey a galaxy undergoes as it evolves through its life cycle. Angelo starts off the episode by asking the question, what's an early-type galaxy? Paolo Bonfini explains that although you may think that early-type galaxies would be galaxies early in their evolution, they're not, they're galaxies a little later. They're the ultimate evolution of two galaxies coming together.
Based on the topics touched on in Paolo's paper he then explains the role that supermassive black holes play in galaxy evolution. Paolo explains, "thanks to the recent development in gravitational-wave astronomy, which opened a completely new window of exploration because it's not based on electromagnetic waves, but on gravitational waves, which are a completely different thing. We are now able to explore black holes in more detail and we're able to study when supermassive black holes merged to create a bigger one."
Relating to the idea of bringing new technology forward, Angelo asks has any computer science techniques assisted you to be able to model this or put it together? Paolo explains, "there are a lot of computations involved in this process. People have in mind the romantic view of the astronomer who just looks through the scope of the telescope and notes things down on a piece of paper, but modern astronomy is completely digitalized. And recently it has been even automated by a lot of procedures that they track and scan the sky to create huge catalogs. Even the images themselves, they are captured on digital devices, like, the same as they appear in the phone, basically, the same technology, but just on a more refined scale. And the first process for which you will need a computer is to combine exposures. So you cannot expose a telescope on a specific direction in the sky for a very long time, for several reasons. The summary is that, in order to take an image of some patch in the sky, you will have to take multiple images and then combine them. Now the modern telescopes, they are extremely accurate. So when you combine them, you need to align the stars to a sub pixel resolution. That means that you have to find the center of the star and itself be positioned within a single individual pixel. And when you combine images, you have to align them by with the precision of, let's say, a third of a pixel, which sounds impossible because you're like, how can you do that? But, there are some techniques that allow you to do that. And of course you need a lot of computational power for that. It can take several minutes to do this even a half an hour, let's say, to combine and produce the image that you see on famous websites, like the Hubble. I mean, this is just the first step. You mentioned a thing you need to actually extract, in my case for the study I was doing, in order to assess the lack of stars at the center of a given galaxy you actually have to measure it. So what you have to do is, you have to trace the light profile, starting from the outskirts of the galaxy going gradually towards the center. In this way, you can draw a light curve if you want. It's not exact, it's more like a light profile. So you have some intensity at the edge of the galaxy, which would be low intensity because the light is very diffused and all the center it grows, grows, grows. And at some point you will see doesn't grow as much. That's where you meet the depleted core, but you also need to quantify this because you want to actually extract the information about the amount of depleted mass, like comments that you would expect it to be versus how many you actually measure. So, you have to fit the light profile. And this is done by, okay. In my case, I've been doing this with some kind of basic statistical technique, which is the chi squared fitting. So you have our model and you just fit the model to the observation and once you have the model, you can project only the other path towards the center and you compare it with the actual model that you fit. And from the difference between the two, you have the amount of stars that are missing. So you need to explore a lot of parameters and therefore you need to have this thing automated via computer technology. There is no chance you can get this information doing it by hand."
Referencing the famous space observatory, Hubble, Pablo explains what it was like to work with such a brilliant piece of machinery. He shares, "it's really amazing because the Hubble telescope was launched in the nineties and just to give you an idea is roughly the size of a bus. There is a replica of it you can visit at, I think it's the Aerospace Museum in Washington, so if you're curious. The main mirror is 2.3 meters in diameter, just to give you an idea, the larger the diameter, the higher the resolution you can achieve. On Earth, there are bigger telescopes. The biggest telescope we have on Earth is currently 10 meters. It's on the Canary Islands. On Earth you have the atmosphere on top of you and this makes everything flicker a little bit because you know, there is air moving, and these big masses of atmosphere move and this shifts the path of the light and this causes the images to be more confused. If you are instead outside the atmosphere, you don't have that problem and you really achieve the limiting resolution of your instrument. So the Hubble Space Telescope is particularly famous because of its resolution. It doesn't have a large collective area, it’s only two meters, let's say, so it doesn't collect a lot of light per second. So it doesn't have, let's say, the same contrast as ground-based telescopes, but it has extremely high resolution. So when you open an image and you're saying, okay, I want to look at this galaxy and I will work on this, which is at the center of the field of view because you pointed there. But, at the edges of it, you see a lot of tiny objects and if you zoom in you can see the structure. Maybe you see a lot of spiral galaxies around the merging objects in the background. And it's not at the center of your research. You're looking at the big galaxy at the center that you're studying. But, you know, it's like a small pleasure, small candy that you have for the eye. You're looking at these things around and you are like, well, man, this is incredible. There are so many things in the universe and I'm here focusing on these big galaxies at the center, but whatever else is happening in the background, and this is really the, I think it's the most impressive thing."
Angelo concludes the episode by discussing the ups and downs of crafting a research paper. Paolo touches on the rollercoaster of emotions one undergoes due to the sheer volume of work that needs to be done. to the most rewarding aspect of writing such a paper. He explains, "you know that you are at the forefront of this research, and I think this is when the reward comes when you're actually presenting and you see the people being curious and asking you directly at the conference, “What is this?” “How did you get there?” “It's very interesting. Let's work together.” “This is an idea to make it even better” and so on."
Our Guest - Thank you!:
Paolo Bonfini - https://www.linkedin.com/in/paolo-bonfini-phd-085a6a179/
Paolo's Paper:
Connecting traces of galaxy evolution: the missing core mass-morphological fine structure relation
Our Team:
Host:Angelo Kastroulis
Executive Producer: Náture Kastroulis
Producer: Albert Perrotta;
Communications Strategist: Albert Perrotta;
Audio Engineer: Ryan Thompson
Music: All Things Grow by Oliver Worth
Angelo: Paolo Bonfini will be joining me today. He’s a Senior Data Scientist and a colleague of mine at Ballista Technology Group. And before working on artificial intelligence and neural networks and solving problems in computational systems and genomics and things like that, Paolo was a master physicist. He received his PhD in astrophysics and he studied that for many years. And so today we’re going to talk about computer science and galaxy evolution. I’m your host, Angelo Kastroulis, and this is Counting Sand.
So, first of all, what's an early type galaxy.
Paolo: So, galaxies in the universe are really a zoo. You can think that each of them is unique. However, we know that they can be grouped roughly, although the boundaries are not really sharp, into different morphological categories. What we call early-type galaxies or late-type galaxies, refer to a classification that dates back to Hubble, in their early 1900s, for a schema that he created and he thought that was the orientation of galaxy evolution—from early galaxies towards late galaxies. We now know the things that are different from the way he envisioned originally, but, the name stayed. So with early-type galaxies we intend a spheroidal galaxy. This is different from what we call a late-type galaxy, which is a spiral galaxy.
As I said, now, we know the evolution goes from spiral galaxy towards spheroidal galaxy. Why? Well, when gas in the universe, assembles to form a galaxy, usually it compresses, basically, simply to the gravitational pull. So it kind of collapses rather than compresses, and in doing so, it might have a rotation and the rotation causes these structures to flatten into a disc.
That's why spiral galaxies which are basically a flat like discs and have spiral arms. These are the galaxies that formed from the original collapse of huge gas clouds. The Milky way, the galaxy we live in, is one of such galaxies. It is a really big one. But not the biggest, the biggest in the universe. So it also happens there are several processes that are still under, you know, they are not yet described completely, but we know roughly that the morphology of galaxies can evolve in time. So our galaxy is not a static object and it can change for different reasons.
For example, you might have internal, shifting of material, for example, we know that spiral arms interact with the remaining gas in the disc of the galaxy and by doing so it also creates a new star and also stars can move along due to internal friction along the spiral arms and converse towards the central bulge.
And so in time the bulge becomes bigger and the galaxy progressively gathers a bulge of stars at the center. But there are also more drastic phenomena like galaxy mergers. You have galaxies that hit each other and merge into a new galaxy. The result of this is basically always an elliptical galaxy or a spheroidal galaxy, they’re called early-type galaxies.
So these are the ultimate products of a galaxy evolution. Just to give you an example, our galaxy, the Milky way, is expected to merge with one other close, massive galaxy, but also a spiral galaxy, which is Andromeda. So these two galaxies are spiraled now and they are going one towards the other and eventually they will merge. They will pass by first, they will have some flybys and then slowly they will spiral in and merge. And it is expected to form a massive early-type galaxy. That explains why spiral galaxies are more massive and the giants of the universe because they come from the merger of other galaxies. So the mass simply sums up.
Angelo: Okay. So that's interesting. So I would have thought early-type galaxies would be galaxies early in their evolution, but they're not, they're galaxies a little later. They're the ultimate evolution of two galaxies coming together.
So in your paper, you talk about, the role that supermassive black holes play in the evolution.
Angelo: Tell me a little bit more about that?
Paolo: Okay. Well, by now we know that basically every galaxy that we know, hosts a supermassive black hole at its center. Not really every galaxy, but let's say, every galaxy with a dignity hosts a supermassive black hole at its center.
What is a supermassive black hole? They come from the collapse of gigantic, massive stars. These are the so-called stellar black holes. Supermassive black holes are a different type of object altogether. It is one of the challenges of modern astronomy to understand the exact nature of the subject, because we still don't know exactly how they form and how they enlarge. Again, they're not objects coming from the collapse of stars. They are much more massive, thousands of times or mass or more. Millions. So we don't know how they form exactly. We didn't know how they grew so fast to become so big and so imposing on the gravity budget of galaxies.
So thanks to the recent development in gravitational wave astronomy, which opened a completely new window of exploration because it's not based on electromagnetic waves, but on gravitational waves, which are a completely
different thing. We are now able to explore this in more detail and especially we're able to study when supermassive black holes merged to create a bigger one.
So we would forget for the moment how they were created in the first place. We just concentrate on how they become even bigger. Similar to two galaxies, when two galaxies merge and they have at their own center two supermassive black holes, eventually these supermassive black holes just because they are the most massive object, they will drift over the center. And this is because of, again, gravitational friction, a supermassive black hole interacts with the stars of the galaxies. And slowly, slowly, they lose energy and converse towards the center where they meet each other in finally merge. In passing, I mentioned that this merger is what generates the emission of gravitational waves.
So this is the target of my study here in my paper. I was trying to combine evidences from the measure of galaxies, which of course disturbed the morphology as we just discussed, with the measure of supermassive black hole at their center.
What happens is this. We have two galaxies merging. As you can imagine as the galaxies pass by each other, they will be completely disturbed and you would have a trails and tails and shelves of stars rebalancing from the newly formed galaxy. So when you take a snapshot of it, which is what we have by looking at the images in the sky, just a snapshot of these events that they last billion of years.
We might be lucky and find some galaxy doing this right now. So well, right then, because we are looking at the past when we look far away, but you know what I mean. We just have this snapshot and we look at this disturbance. Okay. This is a galaxy galaxy undergoing a merger. At the same time, at their center, the supermassive black holes they are spiralling around each other.
And by doing so, as I said, they also interact with the neighboring stars and they kick them around because they transfer their own kinetic energy at their own expense. And that's why eventually they merge into each other. Because they are losing energy, they're falling towards the center center of the galaxy.
And here is the key point. Since these supermassive black holes are so huge compared to a single star. When they interact with the gravitation of one of the stars, the star gets a lot of energy. The supermassive black holes, they lose just a little bit in their binary orbit shrinks a little bit, but the single individual star that
interacted with this binary supermassive black hole gets ejected far out from the center of the galaxy.
So what's happening in these big, big galaxies. They usually are depleted of stars in their center. And there has been a core of studies saying that the origin of these observed lack of stars in the center of the galaxies is related with the activity of these supermassive black holes at the presence, basically.
So this is a result of a series of study that actually led to understand that this thing that we're observing and we didn't know what was causing it. We were projecting the light of the galaxies outside towards inside and you see that at some point there is less than you expect. And this is what we now believe is
happening.
So these two events, the disturbance of the morphology of the galaxy and the creation of depleted core, as we call a lack of stars in the center, it's related. And this is what I actually investigated for the first time observationally in my paper.
Angelo: Yeah. That's a big finding. So it's an important paper. How did computer science help you find this. It seems difficult when you think about looking up at the sky and seeing just stars and kind of putting it together mathematically.
But did you have any computer science techniques you used to come to the conclusion or assist you and to be able to model this or put it together?
Paolo: Well. Let’s say that there are a lot of computations involved in this. People have in mind the romantic view of the astronomer who just looks through the scope of the telescope and, you know, notes things down on a piece of paper, but modern astronomy is completely digitalized.
And recently it has been even automated by a lot of procedures that they track and scan the sky to create huge catalogs. Even the images themselves, they are captured on digital devices, like, the same as they appear in the phone, basically, the same technology, but just on a more refined scale.
And the first process for which you will need a computer is to combine exposures. So you cannot expose a telescope on a specific direction in the sky for a very long time, for several reasons. The summary is that, in order to take an image of some patch in the sky, you will have to take multiple images and then combine them.
Now the modern telescopes, they are extremely accurate. So when you combine them, you need to align the stars to a sub pixel resolution. That means that you have to find the center of the star and itself be positioned within a single individual pixel. And when you combine images, you have to align them by with the precision of, let's say, a third of a pixel, which sounds impossible because you're like, how can you do that?
But, there are some techniques that allow you to do that. And of course you need a lot of computational power for that. It can take several minutes to do this even a half an hour, let's say, to combine and produce the image that you see on famous websites, like the Hubble.
I mean, this is just the first step. You mentioned a thing you need to actually extract, in my case for the study I was doing, in order to assess the lack of stars at the center of a given galaxy you actually have to measure it. So what you have to do is, you have to trace the light profile, starting from the outskirts of the galaxy going gradually towards the center.
In this way, you can draw a light curve if you want. It's not exact, it's more like a light profile. So you have some intensity at the edge of the galaxy, which would be low intensity because the light is very diffused and all the center it grows, grows, grows. And at some point you will see doesn't grow as much.
That's where you meet the depleted core, but you also need to quantify this because you want to actually extract the information about the amount of depleted mass, like comments that you would expect it to be versus how many you actually measure. So, you have to fit the light profile. And this is done by, okay.
In my case, I've been doing this with some kind of basic statistical technique, which is the chi squared fitting. So you have our model and you just fit the model to the observation and once you have the model, you can project only the other path towards the center and you compare it with the actual model that you fit. And from the difference between the two, you have the amount of stars that are missing.
So you need to explore a lot of parameters and therefore you need to have this thing automated via computer technology. There is no chance you can get this information doing it by hand.
Angelo: Okay, that's fascinating. So when you talk about things like chi squared, normally we use that in machine learning all over the place, for
different kinds of, basically trying to fit distributions. Okay. So that's really interesting. So you're using techniques like that.
Do you use any kind of simulation or any predictive capabilities of computer science to come to some of these conclusions. Do you use that anywhere?
Paolo: No in this case. No. But of course there are several areas in astronomy where you do need that. For example, I'm currently involved in another project where we're trying to classify stars based on their properties, their light emission, basically. And this is a classic example of neuron networks where we try to use neural networks as a classifier. So we have some inputs which are the property of the stars—the luminosity in different wave bands. And we try to predict the type of stars because also starts at a different zoo.
They are as complicated as galaxies that are a lot of them, have different properties, which relate with their age, their evolution, and also their context, because maybe some started evolving in environments which are more rich with some materials. So they emit different types of lights and they have emission and absorption paths. And so studying stars and being able to classify them allows you to, again, to start the evolution this time locally, not of the universe, but of the local layer of the galaxy where the stars leave.
Angelo: Yeah, well, I would imagine stars are complicated. They’re like fingerprints, every one is going to be so unique, but trying to classify them seems like an enormous problem or a difficult challenge anyway. What made you want to pursue astronomy.
Paolo: Well, I would say that if I had to study something in real detail, I would like to study the, as is now famous, the theory of everything. If I really had to know something, I want to know where not only we come from, but where everything comes from. And I think this was what was motivating me.
Angelo: Yeah, and of course you've pivoted a little bit. We'll talk about that maybe one of these other days, when we talk about your genomics research and how you kind of pivoted there. How do you think though, that this kind of thinking in astrophysics has influenced the way that you approach other problems. Say, something completely different like genomics or something else.
Paolo: I would say that observational astronomy, which is what I was doing, is different from a theoretical astronomy where people start the cosmology and models of the evolution of the universe. I like to look at the images and extract information from that. I think is not so different from many other branches of
sciences which actually extract information. Basically we are dealing with images. Other people like in bioinformatics are dealing with arrays of numbers, which is the gene expression measured through some techniques. So it is kind of the same. The thing is that I find very found very useful in astronomy is being able to extract until the last tiny bit of information from each observation, because observations are very expensive. For example, if we think of a space telescope, each hour observation can cost millions because you have a lot of people maintaining the space telescope there and then you have a lot of people along the pipeline.
So you don't have the luxury to say, yeah, this doesn't work out, we’ll just take it again. And in fact, when you actually submit a proposal for observations, in any telescope this is true, you also have to predict which is the expected signal that you will extract from this observation that you propose for this many seconds of exposure in the sky.
So this is really an art and it really trains you to find and go at the limit of what the observation, whether it's an image or just a data matrix, can tell you.
Angelo: So it teaches you to have a research driven approach where you're rigorous but then also you're trying to find application, and you're trying to put these two together. Something you just said that was really interesting that I wanted to ask about and that is that, it didn't occur to me and it makes total sense, that a telescope that is orbiting or whatever is a very expensive piece of equipment with a lot of resources behind it. And so there are many proposals, I'm sure, that wants to be able to get a piece, just a few seconds of exposure.
They want to point the telescope and use it. I don't know the process, but it sounds to me like there's someone who is kind of overseeing the use of this telescope, maybe it's NASA, and then you submit a proposal, it gets approved, and it gets scheduled. How does that whole process work? And then the telescope gets pointed and then your time is done and then it moves on to something else.
How does that work exactly?
Paolo: You’ve got it pretty much right. So there is a proposal, which is usually way ahead of the scheduled observations. People can submit the proposals for very important telescopes. The application ratio to successful observation time
is a factor of maybe up to 10—meaning that for 10 people applying one gets time.
So when you apply, you write the scientific motivation for your observation. You also justify why you want to take images of things maybe that have been observed before, but now you want to have a different filter maybe or have a
spectroscopy of some object. And you want to be sure that these things haven't been observed before and they're not in some archive or similar archive to the telescope that you’re waiting for.
So this is step one, then the application gets reviewed. Now they introduced in the most famous space telescope, which is the Hubble Space Telescope and of course my favorite. I mentioned Hubble before, he was one of the key astronomers in history because he basically was the one discovering the expansion of the universe. And the telescope named after him has also been an activity about 25 years now. And he's really revolutionized the way we see the universe.
So I was saying that now the Hubble Space Telescope has a very nice policy, which is a double blind review. You don't know who's reviewing your application and this has been the standard all the time, but also now the reviewer doesn't know your name. And this guarantees that there are no biases, which is a very important topic these days. But it's not just about gender or race. I mean, it is also about scientific bias in the sense that if your name appeared in many publications, it's a somewhat probable that your proposal gets approved.
And this is not fair because you have to evaluate the idea, not the person. So once the set of observations are chosen from different applicants, then there is a scheduler that tries too much time in order to minimize the rotation of the telescope to pass from one target to the other, because there are overheads— pointing the telescope takes time.
But also there are some things that need to be scheduled for specific times, because there are some events like pulsating objects, let's say, and you want to measure them at specific times, so this also must be scheduled inside. Then finally the observations are carried over. And I think usually, it depends on the telescope, but it could be, let's say six months after everything is all right. Also, because once you proposal is approved, then you are asked back to actually give every detail about the objects that you want to point at and for how much time all these days come after. Sometimes you need to create the masks to choose which objects you want to look at in a field.
Finally it is now conventional that the observations are public and it will be like that for the new largest telescope, which is the James Webb Space Telescope. It’s going to be launched actually within this month. So it is now the policy to have everything available right away. In the past, there was a retention period
for which only the observers who actually asked for the observing time and got successful, they were able to access the observation before they went public.
Angelo: So that's good because that means that new potential theories could use the same existing data and they don't have to repoint it. Unless like you said, they want to gather maybe some new filter or some new something or else that wasn't captured in original dataset and they wanted to capture it.
But, that enables a lot of new research. So, so that's pretty cool. Which telescope with this paper did you use to get the data?
Paolo: Well, it was a collection of images, but I think most of them came from the Canadian awaken French. If I remember correctly which is quite the large telescope, quite high tier telescope. It allows and very large, so it allows to collect a lot of light.
And that was fundamental in order to see the fine structure in the morphology of the galaxies, like to see all the tails and shelves and reports on the galaxy. This is really fundamental, I have also been working with Hubble space team.
Angelo: Yeah. So tell me what that's like. You know, that's the most famous telescope. I think most people in the planet know what Hubble is when you mentioned it. What was it like to work with the Hubble.
Paolo: Well, it's really amazing because, so the Hubble telescope was launched in the nineties and just to give you an idea is roughly the size of a bus. There is a replica of it you can visit at, I think it's the Aerospace Museum in Washington, so if you're curious. The main mirror is 2.3 meters in diameter, just to give you an idea, the larger the diameter, the higher the resolution you can achieve. On Earth there are bigger telescopes. The biggest telescope we have on Earth is currently 10 meters. It's on the Canary Islands.
On Earth you have the atmosphere on top of you and this makes everything flicker a little bit, because you know, there is air moving and these big masses of atmosphere move and this shifts the path of the light and this causes the images to be more confused. If you are instead outside the atmosphere, you don't have that problem and you really achieve the limiting resolution of your instrument.
So the Hubble Space Telescope is particularly famous because of its resolution. It doesn't have a large collective area, it’s only two meters, let's say, so it doesn't
collect a lot of light per second. So it doesn't have, let's say, the same contrast as ground-based telescopes, but it has extremely high resolution.
So when you open an image and you're saying, okay, I want to look at this galaxy and I will work on this, which is at the center of the field of view because you pointed there. But, at the edges of it, you see a lot of tiny objects and if you zoom in you can see the structure. Maybe you see a lot of spiral galaxies around the merging objects in the background.
And it's not at the center of your research. You're looking at the big galaxy at the center that you're studying. But, you know, it's like a small pleasure, small candy that you have for the eye. You're looking at these things around and you are like, well, man, this is incredible.
There are so many things in the universe and I'm here focusing on these big galaxy at the center, but whatever else is happening in the background, and this is really the, I think it's the most impressive thing.
Angelo: Yeah, you're getting a small glimpse into all of the things that we haven't even had the chance to research yet and we don't know. It's like all of a sudden your vision is clear for a moment and you can see, wow, there's so many more things than we thought.
What was it like? You know, I think your paper is interesting because it contributes to the knowledge of humanity, kind of moves it forward a little bit. Tell me a little bit about that feeling that you had when you, you know, when it's published and accepted and the fact that you have this feeling of accomplishment that you did something and you contributed something new.
Paolo: Publishing papers is really a rollercoaster of emotions because you have done a lot of work, depending on your efficiency you publish one to three papers per year. If you are extremely good, like top, top, top scientists, you can go beyond that. But I don't consider this a fair ratio in the sense that it looks like you're kind of milking the cow, as you say, like publishing a lot of stuff just because you have a name. But nevertheless, let's say you're spending several months on this project and then you start writing, you go through the reviews with your own collaborators, and then when you think it's ready, you submit, then you wait for the referral report.
And then you'll get the report. If it's positive, you go to the second stage. You make the, you know, the small adjustment that the referee asks you to do. You fix it, second report, maybe third, then you've done. And after that you put it on
the archive and then you wait to see maybe some people will contact you by mail because they saw it right away. So you have the pleasure of like, you know, knowing that somebody will cite your paper. You have the congratulations for the collaborators and so on.
For the contribution to the overall knowledge, I don't think it comes directly from the publication, but rather when you attend the conference and you're presenting your work, and you know that you are at the far edge of the knowledge for this field. There are maybe another four guys on the planet that have your same knowledge on this topic, but everyone else in the room in this specific conference most probably know less than you.
So, you know that you are at the forefront of this research, and I think this is when the reward comes, when you're actually presenting and you see the people being curious and asking you directly at the conference, “What is this?” “How did you get there?” “It's very interesting. Let's work together.” “This is an idea to make it even better” and so on.
Angelo: Yeah. I think for me, the most fun, I think, part of publishing is, for just a minute, you know more about this than anyone else does. Then, of course they'll read it and they'll know about it too. Or at least maybe more than anybody who has said that they know this, you know, maybe somebody knows it and didn't publish it or something, but, you know, that's kind of a neat, you know, being on the cutting edge. I've heard it said a lot that, you know, when you get to the PhD, it's like a razor sharp slice of knowledge that you kind of have, right, on this one, very you go, very deep. Very thin and very deep. Whereas you're trying to cover the breadth earlier, in your master's programs. So I think that's really cool.
Well Paolo, I wanted to thank you very much for the chat today. We’re going to have many more, there’s all kinds of really interesting stuff we can have. I can't wait to talk about genomics and some of the other things. But this is a fascinating paper. I'm going to put it in the show notes and everything too.
Paolo: Thank you very much.
Angelo: I’m your host, Angelo Kastroulis, and this has been Counting Sand. Thank you for joining us today. Before you go, please take a moment to like, review, and subscribe to the podcast. Also, you can follow us on social media. You can find me on LinkedIn @angelok1, feel free to reach out to me there. You can also follow me on Twitter, my handle is @angelokastr. Or you can follow
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