Cities change as they grow -- not only by adding area or population but also in a variety of other ways, from the length and width of their roads to economic growth to the distribution of elementary schools. Social scientists often clash over the best way to measure change as a city swells. Traditionally, they've taken a cross-sectional approach, which means collecting data on a large number of cities of diverse sizes at the same moment in time. More recently, some researchers have begun studying individual cities over time, in what's called temporal scaling.

"These two dimensions, time and population size, need to be treated separately because they express different phenomena," says Luís Bettencourt, an external professor at the Santa Fe Institute and director of the University of Chicago's Mansueto Institute for Urban Innovation. "We need both of them to make sense of what is happening in a complex system like a city."

New work, led by Bettencourt, maps out the common ground between these two approaches. In a paper published this week in the Journal of the Royal Society Interface, the authors argue that while the two methodologies measure different mixtures of the same phenomena, they can be used together to reveal new insights about a city's behavior.

Each approach can be used to calculate an exponent describing the growth rate of some property. (Cross-sectional analyses suggest, for example, that traffic congestion scales exponentially as the size of the city, with an exponent of 7/6.) Those exponents don't necessarily line up, but they don't have to be at odds.

"Now, we're able to have this way to disentangle the two approaches, and bring these two scaling methods back together," says Vicky Chuqiao Yang, an Omidyar Fellow at the Santa Fe Institute who worked on the paper. "With the formalism, we've derived in the paper, we've shown mathematically how these exponents are related between the two approaches."

Scaling behaviors have long been observed and analyzed in physical systems of liquids and gases. Similarly, researchers have long found successful ways to map how properties scale for biological organisms--with the size of animals, for example. "They've compared mice with cows with elephants and found properties that change in a predictable way with size, which spans orders of magnitude," says Yang. But temporal scaling is not obvious in biology, because social systems like cities can grow indefinitely and organisms stop once they reach maturity.

In recent years, as large datasets on urban areas around the world have become available, researchers like Bettencourt and Yang have begun analyzing scaling behaviors that emerge in human systems -- including cities. The field really ignited about a decade ago, she says, when researchers from the Santa Fe Institute first showed that many properties of cities also changed in a predictable way over orders of magnitude in city size. {module INSIDE STORY}

"There was this mysterious phenomenon that the properties of cities change in systematic ways with its size," says Yang. "That included things like fewer gas stations per capita, and a boost in socioeconomic activity, such as more research and development." Since then, researchers have found that many interesting socioeconomic properties increase disproportionally fast with population, said to be "superlinear." Some others grow disproportionally slowly and are said to be "sublinear."

Such scaling behavior has been found in systems ranging from hunter-gatherer societies to modern companies. The new framework offers a way to better understand and quantify properties with systematic trajectories -- and even understand which ones contribute to the health of human institutions. It could, for example, give researchers a way to analyze how a phenomenon like economic growth changes with time and with population size (but does so along both dimensions in different ways). Bettencourt likens the new work to a Rosetta Stone that allows researchers to translate their findings between the two types of scaling.

Brgoch, Wu honored for their work in fundamental chemistry

Two chemists from the University of Houston have been chosen as 2020 Sloan Research Fellows, an honor that recognizes outstanding early-career faculty selected for their potential to revolutionize their fields of study.

Jakoah Brgoch and Judy Wu, both assistant professors of chemistry working in different fields, are among 126 researchers in eight disciplines - ranging from chemistry to neuroscience, physics, and economics - selected for the honor.

"To receive a Sloan Research Fellowship is to be told by your fellow scientists that you stand out among your peers," says Adam F. Falk, president of the Alfred P. Sloan Foundation. "A Sloan Research Fellow is someone whose drive, creativity, and insight makes them a researcher to watch."

Brgoch, whose lab works in both computational and experimental inorganic chemistry, develops materials with applications in energy, manufacturing and other fields. Wu, a computational quantum chemist, is currently working on expanding modern applications of an old chemical concept - aromaticity. {module INSIDE STORY}

Wu said the Sloan Foundation's recognition of fundamental discoveries is encouraging in an era when much of the attention on science has focused on practical applications. "What we are doing is asking a new question of an old concept," she said. "This encourages me to believe the scientific community still values fundamental work. At the core, it is curiosity-driven research."

Wu earned a National Science Foundation CAREER award in 2018 and a National Institute of Health MIRA award in 2019 for her proposal suggesting that connecting aromaticity and hydrogen bonding - previously considered to be separate ideas - could change the way chemists view hydrogen bonds and potentially guide experimental efforts in the design of advanced materials and functional molecules. She continues to work with aromaticity, a fundamental concept in organic chemistry that is usually associated with ring-shaped molecules that increase chemical stability, describing her work as "putting old concepts into a new light."

"There are no dead fields, just new questions," she said. "A lot of these ideas, people think of them as basic concepts in the textbooks. We are showing that they can have practical implications."

Brgoch's lab does both computational and experimental work - using machine learning to predict materials with specific properties followed by synthesizing the material to confirm the predictions. Most researchers specialize in one or the other, collaborating in order to cover the spectrum from prediction to production, but Brgoch teaches his students how to do both.

Doing both in one lab is unusual, but he said it allows his students to see the full process. "It gives a comprehensive and unique perspective to the advantages and disadvantages of both approaches," he said. "They learn what questions to ask and which questions can't be addressed by a calculation or an experiment alone."

He also earned an NSF CAREER award in 2019 for his work in predicting and then synthesizing new compounds for energy-efficient LED-based lighting. There are only a handful of materials used in all of the LED lights around the world, and they are expensive; his research group employs data science to seek cheaper alternatives that outperform current materials.

Winners of the Sloan fellowship receive a $75,000 award to be used to advance their research.

David Hoffman, chairman of the UH chemistry department and himself a Sloan Research Fellow in 1992-94, said the recognition is an acknowledgment of the work done by Brgoch and Wu.

"My colleagues and I in the Department of Chemistry knew early on that Jakoah and Judy were exceptional scientists with all the right attributes to become leaders in their fields," he said. "To have the Sloan Foundation recognize them with fellowships is a wonderful acknowledgment that the scientific community agrees with us. We are fortunate to have them on the faculty at UH."