Now, applied physicists at the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) have invented a new type of interferometer that allows precise control of light’s frequency, intensity and mode in one compact package.

Called a cascaded-mode interferometer, it is a single waveguide on a silicon-on-insulator platform that can create multiple signal paths to control the amplitude and phase of light simultaneously, a process known as optical spectral shaping. By combining mechanisms to manipulate different aspects of light into a single waveguide, the device could be used in advanced nanophotonic sensors or on-chip quantum computing.

Published in Science Advances, the research was led by postdoctoral fellow Jinsheng Lu, who works in the lab of Federico Capasso, the Robert L. Wallace Professor of Applied Physics and Vinton Hayes Senior Research Fellow in Electrical Engineering. Federal support for the work included award No. FA9550-23-1-0699 from the Air Force Office of Scientific Research under. Devices were made at Harvard’s Center for Nanoscale Systems, supported by the National Science Foundation under award No. ECCS-2025158.

“Conceptually, this is a very big step forward compared to the state of the art for commercial high-speed modulators that are particularly used for communications,” Capasso said.

The most widely used such devices, known as Mach-Zehnder interferometers, work by splitting a beam of light down two paths to toggle its output. Despite their widespread use, Mach-Zehnder interferometers have their limitations — they are not very good at simultaneously controlling different aspects of light. Today, multiple interferometers are needed in succession to make up for these limitations, taking up space and restricting the amount of signal that can travel through.

The new cascaded-mode interferometer is a reimagining of a Mach-Zehnder device integrated into a single-chip waveguide. Rather than the traditional split beam, the new interferometer has a unique, nanoscale pattern of gratings etched into the waveguide that control the energy exchange between different modes of light.

This makes the new interferometer able to control the spectrum of light passing through by finely adjusting the intensity and characteristics of different colors. Light can move through in different patterns, or transverse modes. And the device allows for precise, sharp lines of color, or light waves with distinct features.

In the paper, the team not only demonstrates the capabilities of their new interferometer but also lays out the theoretical framework for extending the physics of the device to many different modes of light.

In one, what looks like a pointillist painting illustrates a young zebra finch’s myriad attempts to sound more like an adult, capable of wooing a mate. In another, squiggly lines trace the ebb and flow of chemical signals in the reward circuit of the bird’s brain.

“Their songs don’t sound like much at first,” said Mooney, who has studied birdsong for four decades.

That’s because some things take considerable practice to master. Nobody walks onto a tennis court for the first time and plays a match worthy of Wimbledon, or takes up the piano and becomes a virtuoso overnight.

Likewise, in zebra finches, chicks don’t start out life with the vocal chops to make their signature trills, chirps and peeps. It takes them a while to get the hang of it.

“The amount of effort that a juvenile bird makes to achieve vocal mastery is immense,” Mooney said. “It takes them about one month of solid practice every day, up to 10,000 renditions a day.”

Young finches keep at it hour after hour, day after day, even when no one is listening. Their motivation for mastery comes from within. And now, new research sheds light on the brain signals underlying their intrinsic desire to learn their songs; it also holds implications for understanding human learning and neurological disorders.

Thanks to new tools and techniques, including advances in machine learning and the ability to track subtle and rapid chemical fluctuations in the brain, Mooney and Duke neurobiology professor John Pearson are beginning to disentangle the molecular signals that drive learning for its own sake.

In new research published March 12 in the journal Nature, the team put male juvenile zebra finches into individual soundproof rooms where they could practice their songs at will.

In zebra finches, only the males sing; young birds learn their courtship song early in life by first listening closely to their dad and memorizing his song. Then, like babies learning to talk, they begin to babble, their squeaks slowly becoming more song-like. By practicing their songs and listening to the results, gradually they figure out how to produce the right notes and rhythms to match their mental template of their dad’s song.

It takes a zebra finch chick about three months from hatching to become proficient singers.

To Mooney, a longtime rock ‘n’ roll fan, the males’ practice sessions are a bit like the obsessive recording process for The Beatles. “The Beatles might have done a hundred takes” before they were satisfied, Mooney said. Similarly, “these birdsong data sets get so big so fast.”

That’s where Pearson’s team came in. To get a handle on the data, they developed a machine learning model that can analyze the thousands of song renditions and score each attempt.

“This way we can track learning on a moment-by-moment basis,” Pearson said.

“Some tries were a little better, and some were a little worse,” he added. Generally the longer the birds worked at it, the better they got.

As the birds gradually mastered their tunes, the team also measured the level of dopamine released in the birds’ basal ganglia, a part of the brain involved in learning new motor skills.

Dopamine is one of the brain’s chemical messengers, transmitting important signals about learning, reward and motivation from one neuron to another.

To monitor dopamine, the researchers used tiny sensors made from genetically modified proteins that glow when particular neurochemicals are released in the brain. The technology makes it possible to track brain activity that is largely invisible to common methods based on measuring electrical signals.

What they found surprised them. Whenever a bird practiced, dopamine levels in the bird’s basal ganglia started to ramp up. It didn’t matter whether they hit all the notes or missed the mark. In other words, any effort at singing activates signals in the brain’s reward pathways.

The birds’ dopamine surged more when a bird performed better than was typical for their age. The signal was slightly weaker when they regressed.

The better they performed for their age, the more dopamine increased, said first author Jiaxuan Qi, who did the work as part of her Ph.D. in neurobiology at Duke.

Dopamine has long been known to play an important role in how humans and other animals learn from external rewards and punishments.

Take, for example, a child studying because they want to get a good grade or avoid a scolding. Or consider a rat learning to press a lever for food.

But birds don’t need carrots or sticks to learn how to sing. Because the birds were alone during their practice sessions, singing away in a soundproof room, they weren’t getting any external feedback on how they were doing.

“Nobody’s telling the bird if he’s an honor student or going to be sent to detention,” Mooney said.

Instead, the findings suggest that dopamine acts like an internal “compass” to steer their learning.

The team’s research helps explain how learning still occurs even in the absence of external incentives. The researchers also found that dopamine isn’t the only chemical signal required for such learning.

Qi was able to show that another chemical messenger called acetylcholine can trigger dopamine release in the bird’s brain when it is singing. It works by binding to a different part of the neurons, giving the bird an extra dopamine boost when it belts its ballad.

When the birds were given drugs that blocked dopamine or acetylcholine signaling in the basal ganglia, the birds made less progress, Qi added.

“Learning basically comes to a halt,” Mooney said. “The bird still sings a lot, but he doesn’t seem to be able to learn from it.”

The potential implications go beyond bird brains, Mooney said.

“These findings translate across species,” Pearson said. “The brain regions and neurochemicals involved — namely the basal ganglia, dopamine and acetylcholine — are shared by mice, primates, humans. Essentially every animal with a backbone.”

Studying how birds learn to sing can help researchers better understand how humans learn other motor skills such as talking or juggling or playing an instrument. In that sense, Mooney said, “birdsong learning is very similar to what children do when they spontaneously acquire these remarkable skills.”

Dopamine signaling problems in the basal ganglia have also been linked to a number of diseases, including Parkinson’s and schizophrenia.

“It’s really important that we understand these regions, and the bird is a means of getting at those principles,” Pearson said.

“Of all the scientific frontiers that remain, the brain is probably the most poorly understood, and it’s fundamental to being human,” Mooney said.

This research was supported by grants from the National Institutes of Health (5R01 NS099288, RF1 NS118424, F32 MH132152 and F31 NS132469).

Previous research has shown that interventions grounded in behavioral science that target student motivation have been effective at increasing math scores, suggesting that taking a similar “behaviorally informed” approach with teachers might have a comparable effect.

Now, a collaborative study published in the Proceedings of the National Academy of Sciences, and led by researchers at the Behavior Change for Good Initiative (BCFG) at the University of Pennsylvania has found that behaviorally informed email messages slightly improved students’ math progress compared to control messages.

“Our results showed that simple, low-cost nudges can help teachers support student progress in math,” says Angela Duckworth, Rosa Lee and Egbert Chang Professor in Penn’s School of Arts & Sciences and the Wharton School, who led the study and co-directs BCFG. “These nudges worked across different school contexts, with effects persisting eight weeks after teachers stopped receiving the nudges.”

The key to this megastudy was the partnership with Zearn Math, a nonprofit educational platform. “Large-scale studies on teacher-focused interventions have been rare due to the high cost and logistical challenges involved. Thanks to our partnership with Zearn Math, we were able to overcome these challenges,” says co-author Dena Gromet, executive director of BCFG.

A megastudy is “a large-scale experiment in which multiple interventions are tested simultaneously on the same outcome, a tournament approach, if you will,” says co-author Katy Milkman, James G. Dinan Endowed Professor and professor of operations, information and decisions at the Wharton School and co-director of BCFG. “Because all interventions run concurrently and are compared to a common control group, this method allows for direct comparisons of their effectiveness.”

In one of the largest studies of its kind — involving more than 140,000 teachers and nearly 3 million elementary students — the researchers compared the impact of 15 different interventions to a reminder-only message.

“These messages were behaviorally informed, meaning they were based on prior insights from behavioral science. For instance, one intervention asked teachers to make a specific plan for how they would use Zearn Math that week, an approach backed by research showing that people are more likely to follow through when they make detailed plans. Another intervention appealed to teachers’ empathy for their students, which previous research has demonstrated is supportive of student success,” Duckworth says.

Co-authors Katy Milkman (left) and Angela Duckworth are committed to dig deeper into what makes these kinds of interventions work and how to make them even more effective over time.

Specifically, the research team found that, compared to standard email reminders, behaviorally informed email messages improved students’ math progress during the four-week intervention period by 1.89%. The most effective intervention, which increased student math progress by about 5.06%, encouraged teachers to log into Zearn Math weekly for an updated, personalized report on their students’ progress.

“One especially promising takeaway is that personalized nudges — those that referenced progress updates about a teacher’s own students — were more effective than nonpersonalized ones,” Duckworth says.

The researchers note that though they are promising, the effects were small. “These results suggest the need for more intensive support than the light-touch email nudges we tested,” Milkman says. “And they underscore how hard it is to change human behavior.”

These findings, Milkman says, suggest several additional valuable avenues for future research, including “more random-assignment field experiments to confirm the causal benefits of teacher-targeted nudges and studies to probe the longer-term effects of behaviorally-informed interventions.”

Additional research is also needed, Duckworth says, “to confirm and explain the benefits of referencing personalized data when nudging teachers. It may be that capitalizing on teachers’ intrinsic motivation to help their students is a distinct and potentially cost-effective approach that can complement other interventions, such as offering performance bonuses and other extrinsic incentives.”

Next steps for researchers are to dig deeper into what makes these kinds of interventions work and how to make them even more effective over time. Future studies are needed to look into the long-term effects of nudges and explore why some interventions are more effective than others.

“The better we understand why something works, the more powerfully we can use it to create positive change,” Duckworth says. “Ultimately, this line of research could help shape smarter, more effective education policies.”

Angela L. Duckworth is the Rosa Lee and Egbert Chang Professor in the Department of Psychology in the School of Arts & Sciences and in the Department of Operations, Information, and Decisions in the Wharton School at the University of Pennsylvania and faculty co-director of the Penn-Wharton Behavior Change for Good Initiative.

Katherine L. Milkman is the James G. Dinan Endowed Professor in the Department of Operations, Information, and Decisions in the Wharton School of the University of Pennsylvania and faculty co-director of the Penn-Wharton Behavior Change for Good Initiative.

Dena M. Gromet is the Executive Director of the Behavior Change for Good Initiative at the University of Pennsylvania.

Other authors of the new study are Ron Berman, Eugen Dimant, Ahra Ko, Joseph S. Kay, Youngwoo Jung, Madeline K. Paxson, Ramon A. Silvera Zumaran, and Christophe Van den Bulte of the University of Pennsylvania; Aden Halpern of the University of Pennsylvania and the University of Pittsburgh; Nina Mazar of Boston University; Colin F. Camerer and Marcos N. Gallo of the California Institute of Technology; Amy Lyon of Colby-Sawyer College; Mary C. Murphy of Indiana University; Kathryn M. Kroeper of Sacred Heart University; Benjamin S. Manning of the Massachusetts Institute of Technology; Ilana Brody, Hengchen Dai, and Hal E. Hershfield of the University of Los Angeles; Ariel Kalil, Michelle Michelini, and Susan E. Mayer of the University of Chicago; Matthew D. Hilchey, Philip Oreopoulos, Renante Rondina, and Dilip Soman of the University of Toronto; Elizabeth Canning of Washington State University; and Sharon E. Parker of Philadelphia.

Research reported in this article was supported in part by an anonymous donor to Zearn Math. Support for this research was also provided in part by the AKO Foundation, J. Alexander, M. J. Leder, W. G. Lichtenstein, and A. Schiffman and J. Schiffman.

In the shallow waters of the Lighthouse Reef Atoll, located 80 kilometers off the coast of the small Central American country of Belize, the seabed suddenly drops steeply. Resembling a dark blue eye surrounded by coral reefs, the “Great Blue Hole” is a 125-meter-deep underwater cave with a diameter of 300 meters, which originated thousands of years ago from a karst cave located on a limestone island. During the last ice age, the cave’s roof collapsed. As ice sheets melted and global sea level started to rise, the cave was subsequently flooded.

In the summer of 2022, a team of scientists — led by Prof. Eberhard Gischler, head of the Biosedimentology Research Group at Goethe University Frankfurt, and funded by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) — transported a drilling platform over the open sea to the “Great Blue Hole.” They then proceeded to extract a 30-meter sediment core from the underwater cave, which has been accumulating sediment for approximately 20,000 years. The core was subsequently analyzed by a research team from the universities of Frankfurt, Cologne, Göttingen, Hamburg, and Bern.

Coarse layers are a testimony to tropical storms

Some 7,200 years ago, the former limestone island of what is now Lighthouse Reef was inundated by the sea. The layered sediments at the bottom of the “Great Blue Hole” serve as archive for extreme weather events of the past 5,700 years, including tropical storms and hurricanes. Dr. Dominik Schmitt, a researcher in the Biosedimentology Research Group and the study’s lead author, explains: “Due to the unique environmental conditions — including oxygen-free bottom water and several stratified water layers — fine marine sediments could settle largely undisturbed in the ‘Great Blue Hole.’ Inside the sediment core, they look a bit like tree rings, with the annual layers alternating in color between gray-green and light green depending on organic content.” Storm waves and storm surges transported coarse particles from the atoll’s eastern reef edge into the “Great Blue Hole,” forming distinct sedimentary event layers (tempestites) at the bottom. “The tempestites stand out from the fair-weather gray-green sediments in terms of grain size, composition, and color, which ranges from beige to white,” says Schmitt.

The research team identified and precisely dated a total of 574 storm events over the past 5,700 years, offering unprecedented insights into climate fluctuations and hurricane cycles in the southwestern Caribbean. Instrumental data and human records available to date had only covered the past 175 years.

Rising incidence of storms in the southwestern Caribbean

The distribution of storm event layers in the sediment core reveals that the frequency of tropical storms and hurricanes in the southwestern Caribbean has steadily increased over the past six millennia. Schmitt explains: “A key factor has been the southward shift of the equatorial low-pressure zone. Known as the Intertropical Convergence Zone, this zone influences the location of major storm formation areas in the Atlantic and determines how tropical storms and hurricanes move and where they make landfall in the Caribbean.”

The research team was also able to correlate higher sea-surface temperatures with increased storm activity. Schmitt states: “These shorter-term fluctuations align with five distinct warm and cold climate periods, which also impacted water temperatures in the tropical Atlantic.”

Climate change results in greater storm activity

Over the past six millennia, between four and sixteen tropical storms and hurricanes passed over the “Great Blue Hole” per century. However, the nine storm layers from the past 20 years indicate that extreme weather events will be significantly more frequent in this region in the 21^st century. Gischler warns: “Our results suggest that some 45 tropical storms and hurricanes could pass over this region in our century alone. This would far exceed the natural variability of the past millennia.” Natural climate fluctuations cannot account for this increase, the researchers emphasize, pointing instead to the ongoing warming during the Industrial Age, which results in rising ocean temperatures and stronger global La Niña events, thereby creating optimal conditions for frequent storm formation and their rapid intensification.

MIT instructor Karol Bacik and his colleagues studied the flow of human crowds and developed a first-of-its-kind way to predict when pedestrian paths will transition from orderly to entangled. Their findings may help inform the design of public spaces that promote safe and efficient thoroughfares.

In a paper appearing in the Proceedings of the National Academy of Sciences, the researchers consider a common scenario in which pedestrians navigate a busy crosswalk. The team analyzed the scenario through mathematical analysis and simulations, considering the many angles at which individuals may cross and the dodging maneuvers they may make as they attempt to reach their destinations while avoiding bumping into other pedestrians along the way.

The researchers also carried out controlled crowd experiments and studied how real participants walked through a crowd to reach certain locations. Through their mathematical and experimental work, the team identified a key measure that determines whether pedestrian traffic is ordered, such that clear lanes form in the flow, or disordered, in which there are no discernible paths through the crowd. Called “angular spread,” this parameter describes the number of people walking in different directions.

If a crowd has a relatively small angular spread, this means that most pedestrians walk in opposite directions and meet the oncoming traffic head-on, such as in a crosswalk. In this case, more orderly, lane-like traffic is likely. If, however, a crowd has a larger angular spread, such as in a concourse, it means there are many more directions that pedestrians can take to cross, with more chance for disorder.

In fact, the researchers calculated the point at which a moving crowd can transition from order to disorder. That point, they found, was an angular spread of around 13 degrees, meaning that if pedestrians don’t walk straight across, but instead an average pedestrian veers off at an angle larger than 13 degrees, this can tip a crowd into disordered flow.

“This all is very commonsense,” says Bacik, who is a instructor of applied mathematics at MIT. “The question is whether we can tackle it precisely and mathematically, and where the transition is. Now we have a way to quantify when to expect lanes — this spontaneous, organized, safe flow — versus disordered, less efficient, potentially more dangerous flow.”

The study’s co-authors include Grzegorz Sobota and Bogdan Bacik of the Academy of Physical Education in Katowice, Poland, and Tim Rogers at the University of Bath in the United Kingdom.

Right, left, center

Bacik, who is trained in fluid dynamics and granular flow, came to study pedestrian flow during 2021, when he and his collaborators looked into the impacts of social distancing, and ways in which people might walk among each other while maintaining safe distances. That work inspired them to look more generally into the dynamics of crowd flow.

In 2023, he and his collaborators explored “lane formation,” a phenomenon by which particles, grains, and, yes, people have been observed to spontaneously form lanes, moving in single-file when forced to cross a region from two opposite directions. In that work, the team identified the mechanism by which such lanes form, which Bacik sums up as “an imbalance of turning left versus right.” Essentially, they found that as soon as something in a crowd starts to look like a lane, individuals around that fledgling lane either join up, or are forced to either side of it, walking parallel to the original lane, which others can follow. In this way, a crowd can spontaneously organize into regular, structured lanes.

“Now we’re asking, how robust is this mechanism?” Bacik says. “Does it only work in this very idealized situation, or can lane formation tolerate some imperfections, such as some people not going perfectly straight, as they might do in a crowd?”

Lane change

For their new study, the team looked to identify a key transition in crowd flow: When do pedestrians switch from orderly, lane-like traffic, to less organized, messy flow? The researchers first probed the question mathematically, with an equation that is typically used to describe fluid flow, in terms of the average motion of many individual molecules.

“If you think about the whole crowd flowing, rather than individuals, you can use fluid-like descriptions,” Bacik explains. “It’s this art of averaging, where, even if some people may cross more assertively than others, these effects are likely to average out in a sufficiently large crowd. If you only care about the global characteristics like, are there lanes or not, then you can make predictions without detailed knowledge of everyone in the crowd.”

Bacik and his colleagues used equations of fluid flow, and applied them to the scenario of pedestrians flowing across a crosswalk. The team tweaked certain parameters in the equation, such as the width of the fluid channel (in this case, the crosswalk), and the angle at which molecules (or people) flowed across, along with various directions that people can “dodge,” or move around each other to avoid colliding.

Based on these calculations, the researchers found that pedestrians in a crosswalk are more likely to form lanes, when they walk relatively straight across, from opposite directions. This order largely holds until people start veering across at more extreme angles. Then, the equation predicts that the pedestrian flow is likely to be disordered, with few to no lanes forming.

The researchers were curious to see whether the math bears out in reality. For this, they carried out experiments in a gymnasium, where they recorded the movements of pedestrians using an overhead camera. Each volunteer wore a paper hat, depicting a unique barcode that the overhead camera could track.

In their experiments, the team assigned volunteers various start and end positions along opposite sides of a simulated crosswalk, and tasked them with simultaneously walking across the crosswalk to their target location without bumping into anyone. They repeated the experiment many times, each time having volunteers assume different start and end positions. In the end, the researchers were able to gather visual data of multiple crowd flows, with pedestrians taking many different crossing angles.

When they analyzed the data and noted when lanes spontaneously formed, and when they did not, the team found that, much like the equation predicted, the angular spread mattered. Their experiments confirmed that the transition from ordered to disordered flow occurred somewhere around the theoretically predicted 13 degrees. That is, if an average person veered more than 13 degrees away from straight ahead, the pedestrian flow could tip into disorder, with little lane formation. What’s more, they found that the more disorder there is in a crowd, the less efficiently it moves.

The team plans to test their predictions on real-world crowds and pedestrian thoroughfares.

“We would like to analyze footage and compare that with our theory,” Bacik says. “And we can imagine that, for anyone designing a public space, if they want to have a safe and efficient pedestrian flow, our work could provide a simpler guideline, or some rules of thumb.”

This work is supported, in part, by the Engineering and Physical Sciences Research Council of UK Research and Innovation.