Fractals Within Us

 This is a special guest blog article by Jiyeong Kim, a 3rd year PhD student in Computational Physics Laboratory at Tampere University in Tampere, Finland. Her research topics are time-series analysis and nonlinear dynamics in biological and financial systems. She can be reached at jiyeong.kim@tuni.fi. 

When you think of the word fractal, you probably have certain images immediately coming to your mind: infinitely continuing patterns and swirls! I find them fascinating and quite beautiful, especially when they are created in nature. Common examples of fractals in nature are snowflakes, tree branches, and Romanesco broccoli. Now, these are geometric fractals, but the concept of fractals is not limited to geometry. 

 

Romanesco broccoli. Photo by Aurelien Guichard
Flickr: Borough Market

The definition of a fractal is a structure that displays self-similar patterns across different scales. For geometric fractals, the scale is spatial one, but the scale can also be time. Temporal fractals are fluctuations that are statistically similar over multiple time scale; that is, when you look at a fractal signal at different scales, whether it’s 3 minutes, 30 minutes, or 3 hours, the fluctuations are similar. This type of signals are also known as 1/f noise, or pink noise.

What’s really fascinating about the 1/f noise is that it appears in many biological systems, including us humans, and it also seems to play an important role in our health. The most famous example of 1/f noise is our heartbeat. Even though many people believe that our heart rate should be regular (apart from it changing due to activities such as exercise or sleep), this is far from the truth.

Take a look at the figure below. Can you guess which one belongs to a healthy person?

Which one belongs to a healthy person?
Image: Goldberger et al., PNAS February 19, 2002 99 (suppl 1) 2466-2472

The correct answer is B! If you got it right, I am very impressed. When we showed these graphs to a group of cardiologists, not everyone got it right either. A and C belong to patients with several congestive heart failure syndromes, and D to a patient with atrial fibrillation.

So our heart rate, it turns out, fluctuates in a very complex manner that is neither too regular nor too random--it’s fractal! Having a fractal structure is often related to the system’s robustness against external stress; that is, our heart can adjust to sudden changes better in the presence of fractal dynamics. Many scientists have confirmed the presence of fractality and its alteration due to aging and heart diseases. Though fractal analysis is not used yet in clinical practices, it has a great potential as a noninvasive diagnostic tool. Who knows? All the handy heart monitoring devices out there may soon add a feature that tells you how fractal your heart rate is!

Heartbeat is not the only thing that is fractal within us. Respiration rate, blood pressure, gait (stride-to-stride fluctuation), glucose level, gene expression, DNA sequences...the list goes on. One I find especially interesting is finger tapping.

When you tap your finger to a certain tempo, you can imagine that it won’t be perfect like a metronome. Its deviations from the intended beats (the metronome) have fractal structure. A similar phenomenon also occurs in drumming. When a drummer performs, no matter how hard he/she tries, there are always some deviations from the exact beat, which turn out to be also fractal. The importance of the fractal deviations in drumming was revealed in a survey. Between two humanized drumming samples, one with Gaussian fluctuations and the other with 1/f fluctuations, many preferred the latter. In other words, the presence of 1/f fluctuations makes music sound more human.

A recent study conducted with a real-world data analyzed the song I Keep Forgettin’ (1982) by Michael McDonald. The drummer in the song is Jeff Porcaro (1954-1992), who was a session musician behind many recordings of, e.g., Michael Jackson and Madonna, and a member of major rock bands Steely Dan and Toto. The song features Porcaro’s well-known single-handed hi-hat technique that is particularly smooth and groovy; it’s the really fast, high-pitched beats in the background, if you are listening to the song. Guess what they found? 1/f fluctuations in both intervals and amplitude. The study implies that behind the groovy feel of a good drummer is the naturally occurring fractal fluctuations in the rhythm.

What you also need to know is that the 16th notes Porcaro plays is about 150 ms apart, and deviation is only about 20 ms. That is, there should be no way that we can detect the deviations with our ears. But somehow we can tell from the groovy feel that something is there. So the ‘groove’ is somehow also related to how we perceive the timing and rhythm. Could it be related to the fact that the nerve spike intervals have fractal fluctuations?

We continue to discover fascinating fractal phenomena and there are still many questions to be answered. Many researchers are working towards unlocking the secrets of fractal dynamics in human body, in nature (temperature, precipitation, ozone level, climate dynamics), and in our society (internet traffic, highway traffic, stock market dynamics, they all exhibit fractal fluctuations!). One of the biggest question in the studies of fractal time series is certainly the origin of fractality. Recent studies, including my own, have shown that we can find fractal dynamics even at the cellular level; clusters of heart cells, grown from stem cells in laboratory, beat together spontaneously exhibiting fractal-like fluctuations in their beat rates without any neural input. Looks like we are full of fractals all the way down to our cells!

Sources:

https://www.sciencemag.org/news/2015/06/secret-groovy-drumming-may-be-math

https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0127902#sec002

https://www.pnas.org/content/99/suppl_1/2466

I Dug Up a Camel: Part 2

Last week's blog post was about the history of camels in the American southwest and how I found myself at a prehistoric camel dig in the middle of eastern Arizona. This week I'm excited to show pictures from the dig and explain the process of taking an ancient camel skeleton out of the desert and into the lab. First, a quick summary of our camel. We estimate that it's about 2.2 to 2.4 million years old, it is one of three camels (and a turtle) found in a small area, it's a sub-adult camel, and its skeleton is complete, meaning that almost all of the bones, from the head to the tail, were found at the same time. All of these details make our camel a rare find, so we want to take extra special care of it.

Me in the field out at the camel dig site. The turtle shell is about
200 feet behind me, and the camel is about 15 feet in front of me.
PC: Jessica Noviello, Nov. 2018.

On a bright but cold Saturday morning, we piled into pickup trucks with our rock hammers, flathead screwdrivers, hats, jackets, and sunblock and drove out to the dig site. Our group numbered about 15 people, ranging in age from a young boy of 10 to Larry, our senior expert from the local Bureau of Land Management Office. Most of us were volunteers eager to get experience at a real paleontology dig. Two expert paleontologists from the Arizona Museum of Natural History also came along to supervise and give us geologic context. To go out on a dig like this, everyone needs to have at least some experience working with fossils, and everyone must be able to work together as a team, or else we run the risk of damaging or destroying the bones.

I spent most of my weekend working on excavating the camel. Larry had already spent time uncovering it, and previous volunteer teams had already taken the skull and neck, two of the legs, and the hips out of the field. Our goal for the weekend was to remove the torso, and maybe start on getting another leg out of the rock and sand. Others worked on excavating the turtle shell (carapace), a large dome that was roughly 2 feet in diameter. Still others spent time walking around looking for other bone fragments and maybe teeth, a process called prospecting.

Step 1: We used toilet paper and field "glue" to stabilize the fragile
parts of the camel torso. PC: Jessica Noviello, Nov. 2018.

There's a big difference between reading about digs and actually being on a dig. I think what surprised me most is how many everyday items are used in paleontology, the first example of which was toilet paper. After we removed the surrounding dirt from the torso but before we could wrap the bones in plaster, we first had to stabilize and protect them from the plaster itself. We did this by gently placing toilet paper on the particularly fragile bits of the camel torso and wetting the paper with a liquid mixture of water and acetate, which we called field "glue."

Dipping burlap strips into the plaster to lay on the camel torso.
PC: Jessica Noviello, Nov. 2018.

Next we had to wrap the torso up in plaster to protect it on its journey from desert to museum lab. One volunteer, Emelia, was in charge of making the mixture of plaster and water the exact right consistency, which she called "pancake batter." Another volunteer, Alex, was in charge of ripping up burlap cloth. These burlap strips were dragged through the plaster mix and laid on the torso. We applied at least two layers of burlap and plaster to the entire torso, taking special care around the fragile bits. Finally, we put two wood planks onto the top of the torso, which makes the torso easier to carry and move.

The camel torso ready to be flipped! Rock hammer and blue
stuffed dinosaur for scale. PC: Jessica Noviello, Nov. 2018.

Removing the torso wasn't as easy as just picking it up from the dirt, however. There was still half the torso connected to the dirt underneath the bit we had already excavated. The only solution, therefore, was to flip the torso over. We did this by literally hammering a long rod underneath the torso and using it as a lever. I left the more experienced volunteers to the flipping so I could film it. I was surprised at how quickly it happened. We spent hours preparing the torso, but the actual act of flipping only took about 3 seconds. It was as easy as lifting up on the lever, catching the torso, and lowering it down onto the tarp we had laid out. The tarp allowed us to pick up the entire torso without directly touching it, potentially putting pressure on a weak point in the plaster. Speaking from experience, the tarp made it much easier to carry the torso back out to the cars, though we still needed 4 people to do it.

After we flipped the torso, we were relieved to see that the rod hadn't hit any of the remaining bones, particularly the two legs that were wedged underneath the torso. We were basically drilling blind, so we got really lucky! Unfortunately, the entire torso didn't survive the flip, and some bits and pieces were left behind. We spent the rest of that Saturday closely examining the dirt that was left behind, searching for bone fragments or even some skin impressions. The biggest pieces that were left behind were the ribs, which needed their own plaster jacket before they were moved. You saw these in Part 1 of this blog post.

Bone fragments I picked up while prospecting. Notice the
slight purple tinge and the shiny nature of the bones.
PC: Jessica Noviello, Nov. 2018.

By Sunday there wasn't much left to do on the camel, so I jumped between excavating the turtle shell and prospecting. At first I had a terrible time prospecting. The bone fragments were small and fragmented, so they camouflaged perfectly with the surrounding gravel. I quickly grew frustrated. Thankfully, another member of the Southwest Paleontological Society, Jenny, found a small area that had a bunch of bone fragments, so she called me over to help. I always thought that people exaggerated when they say "once I found one, I easily found tons more," but that's exactly what happened. The bone shards had a slightly purple tinge and a shiny luster that the dull gravel lacked. Once I knew what I was looking for, I couldn't walk two steps without finding more. We carefully put all the fragments into Ziploc bags and labeled them clearly so we had a good record of our data. These bones and bone fragments are true data, evidence of ancient life and a world that doesn't exist anymore. We don't get a second chance to find these if they are lost or destroyed, so we take the process seriously.

Soon after we packed up and covered the remainder of the camel with sand, to be dug up by future groups. The rest of the camel and the turtle headed back to Mesa, where more volunteers would remove the plastic and clean up the bones. I had a great time going out on my first paleontology dig, and if I wasn't in a desperate rush to finish my PhD this spring, I'd be going out again to finish the job. If you are interested in participating in a paleontology dig, I'd first suggest reading up on the subject, and then reaching out to a local museum to get experience working with fossils or in a lab. It is definitely a special experience, and one I am so thankful to have. At the very least, it makes for a great adventure story!

Me digging out the camel torso and preparing it to be flipped.
This is why we use flathead screwdrivers!
PC: Jessica Noviello, Nov. 2018.

I Dug Up a Camel: Part 1

Sometimes the best science opportunities suddenly appear in front of you. In those instances, the best thing to do is say yes and embrace the experience that will one day make a grand adventure story. In November 2018, one of these opportunities knocked me off my feet, literally.

I was training in my Krav Maga class with my partner, an older man named Sherman, and a fellow graduate student, Mariah. We were working on defending against aggressive knife techniques, and one of the defenses ends up with the attacker on the ground, which is how I found myself looking up at my partners with the wind knocked out of me. As I stood up and caught my breath, Sherman asked Mariah and me if we liked paleontology. Turns out Sherman is the President of the Southwest Paleontological Society (SPS), and because he knew that Mariah and I are geology graduate students, he invited us both out to a paleontology dig in eastern Arizona in mid-November. A little over a week later I was in a car driving out to a campground in Safford, Arizona. The hunt for bones was on! Our quarry: a prehistoric camel.

The view from our campground on this dig near Safford, AZ.
PC: Jessica Noviello, 2018.

Our housing at the campground. I was prepared for a tent, but this works too!
PC: Jessica Noviello, 2018.

 Camels have a long history in Arizona that begins 45 million years ago in the Eocene period. Back then, Arizona was a rainforest, and the place where a small, deer-like animal made its appearance in the fossil record: Protylopus. This is the earliest known camel, and its discovery surprised paleontologists. Modern camels, and even most fossil camels, have cushioned, wide feet to help them move over unstable terrain like sand and grassland gravel. But Protylopus walked on four dainty toes on each foot. As southwest North America changed from rainforests to grasslands, these feet put the Protylopus at a mobility disadvantage, and they couldn't overcome it. They eventually died out, but not before starting the lineages that would eventually lead to modern camels.

Artist's reconstruction of Protylopus in its habitat.
PC: WILLEMSVDMERWE and PBS: Eons.

Ancient camels eventually traveled north and west across the landbridge that spanned the Bering Strait, into Asia and Europe, where they became the modern camels we know today. North America and South America finally connected to form the isthmus of Panama around 3 million years ago, leading to a significant migration event called the Great American Interchange. Species that had evolved on one continent quickly moved to the other, including some camels. The camels that migrated south would eventually evolve into the ancestors of llamas and alpacas.

Our camel died after this Interchange event, sometime between 2.2 and 2.4 million years ago. It belonged to the Camelops genus, enormous animals that stood 11.5 feet tall as adults, almost twice as tall as today's camels. Camel skeletons and bones are fairly common throughout the American west, but our camel was unusual for a few reasons. One, our camel was a sub-adult, or a camel teenager; two, our camel was one of three found within a 200 span of an ancient river bed; and three, our camel was complete.

Rib bones of our camel. PC: Jessica Noviello, 2018.

In paleontology, a complete skeleton is one where all of the bones from the skull to the tail are found together, including the small bones found at the ends of the limbs. Turning a dead animal into a fossil takes a long time that ranges from thousands to millions of years depending on the environment. During this time period, scavengers can take bones away from the rest of the skeleton, and natural catastrophes like floods and mudslides can wash bones away.

Finding an entire skeleton is rare. Our camel is only the third complete camel discovered so far in the entire southwest! For this camel to also be a sub-adult makes it even more valuable, as it shows us exactly what that animal looked like at its stage in development as it grew from baby to adult. Its completeness indicates it was buried quickly, before anything could move the bones away. The fact that it was found with two other camels (and an ancient turtle too!) in an old riverbed points to a sudden event, like a flash flood, as the cause of death.

What was it like to dig up the camel? What are the steps involved? Who does stuff like that on their weekends? Find out in Part 2 of this blog post, coming next week!

Additional source:
"When Camels Roamed North America." PBS: Eons. November 20, 2018. https://www.youtube.com/watch?v=lJNoAE0UHzY

Scientific Conferences: AGU 2018

Happy New Year! We here at Science on Main hope you all have a great 2019!

For such a big part of an academic's life, conferences are rarely written about in the world of science communication. The to-do list of things just to attend conferences is long before an attendee even gets there: writing the abstracts, registering, making lodging and travel reservations, doing the proposed work, preparing the posters and oral presentations, and setting up meetings with colleagues are all part of conferences, and that's on top of the official stuff like sessions and workshops! But what happens at these conferences? What's the point of going to them at all? What are they like?

Granted, I can only speak to my own personal experiences at conferences, and each conference has its own particular feeling and style. Some things are similar for all though. It's usually hundreds, if not thousands of people who are all interested in a particular subject arriving at one location to speak to each other face to face. These are not just scientists, as the conferences I go to also have industry representatives who are there to both recruit new employees and sell their company's products. Conferences usually last for a whole work week, and if it's in a new city, I'll try to go at least one day early or stay a day later so I can do some exploring. I know I'm not the only one who does that. It's fun to explore a new city, or even a new country, like I did when I went to Rome, Italy to participate in a conference hosted by the European Space Agency.

The #AGU100 sign outside of the Exhibit Hall at this year's conference.

 The conference I went to in December 2018 was the American Geophysical Union (AGU) Fall Conference in Washington, D.C. It's by far the largest conference I go to because it spans all fields related to geoscience on Earth and elsewhere in the solar system (which is my field: planetary science). This year was special because it was AGU's centennial year, and they were definitely celebrating it. At least 27,000 scientists, exhibitors, students, professionals, volunteers, and organizers came to the nation's capital to share their results and network. Off the top of my head I can't list every discipline represented, but here are a few: planetary scientist, educators, atmospheric chemists, heliophysicists (they study the sun), seismologists, oceanographers, computer scientists, and statisticians. The other main conference I go to is only planetary science, and more specialized conferences mean fewer people attend. It's always good to dive deep into my subject, but I like AGU because it allows me to see techniques and ideas in other fields too.

Perhaps a third of the posters in the poster hall at #AGU100.
I'm guessing the whole thing was 1/4 mile long!

One of the best parts of conferences is how many events there are to go to at any given time, which means everyone can pick and choose what they want to attend. That choice can be a double-edged sword too, since going to one thing means saying no to potentially several others. I try to find friends who will either tweet or take extensive notes during their sessions, that way I never miss anything! This year at AGU I made sure to spend time in a few of the science communication workshops that the Sharing Science division puts on every year, including one that taught me the technical details of how to start a podcast. I came away invigorated and excited to pursue new ideas! This is in addition to the dozens of talks and posters I saw, the volunteering I did at the Arizona State University booth, and the one-on-one meetings I had, of course.

The AGU booth was selling stuffed owls in
sweatshirts. I couldn't resist. It was so cute!
I named him Dr. Whoot.

Speaking of the meetings, that's another major positive about conferences, especially for people who, like me, are approaching graduation and are looking to move to a new position at a new place. At AGU, I was able to meet with senior scientists from all over the country, including NASA Headquarters, to talk to them about potential positions for me. Conferences give young scientists a chance to display their body of work to the entire community and to make connections that will last years, perhaps decades, and many projects. I know of a post-doc who was offered a job the day after he gave his talk, which would not have happened without a conference. For people who are working on projects together, it is always more efficient to meet in person instead of emailing, as questions and concerns are addressed immediately. It improves the quality of the science done too!

Conferences are exhausting and crazy, but they are essential for science to grow and continue. To be able to talk to experts directly about their work increases my knowledge about the field and shows me what work needs to be done in the future. I also gained new collaborators and friends. I've only shared a fraction of the stories I got at this year's AGU, but I hope it was enough to show you a little of what a science conference is all about!