Researchers created a mathematical model that helps transplant centers make decisions about when to move forward with a matching donor and when to wait. This work can potentially help decision making in other industries. Photo via Getty Images

To wait, or not to wait? That is the question — or at least it might be, if you need a kidney transplant.

Nearly 89,000 Americans with chronic kidney disease are on a waitlist for a new organ, and an estimated 13 people die each day while awaiting a transplant. But there are real costs to matching patients with the first donor that becomes available, just as there are equally real costs to having them wait in hopes of finding a better one.

Recently, Rice Business professor Süleyman Kerimov and colleagues at Stanford University and Northwestern University developed a mathematical model that helps clarify when it's best to match patients to donors as quickly as possible and when it's best to wait.

Their findings, which appear in two papers published in Management Science and Operations Research, respectively, could help optimize all manner of matching markets in which participants seek to connect with potential partners based on mutual compatibility — a sprawling category that encompasses everything from e-commerce platforms to labor markets that match employees with employers.

Kerimov and his colleagues focused on programs that match live kidney donors with people who need transplants. Live donors typically volunteer to give one of their kidneys to a loved one. But biological differences between a donor and their intended recipient can render the pair incompatible.

Kidney exchange programs solve this problem by swapping donors amongst different patient-donor pairs, choreographing a kind of kidney-transplant square dance aimed at finding a compatible partner for every willing donor.

In countries such as Canada and the Netherlands, kidney-matching programs perform a batch of matches every few months (called periodic policies). American programs, meanwhile, tend to perform daily matches (called greedy policies). Both models seek to produce the greatest number of high-quality transplants possible, but they each have advantages and disadvantages.

Less frequent matches in a periodic policy allow more patient-donor pairs to accumulate in the kidney exchange network, creating potential for better matches over time. But this approach risks making some patients sicker as they wait for a better match that might never appear.

Arranging feasible matches as soon as they become available in a greedy policy avoids that predicament. But it means passing up the opportunity to make a potentially better match that could represent the possibility of a longer, healthier life.

Balancing these trade-offs is tricky. There is no way of predicting precisely when a patient-donor pair with a particular set of characteristics will show up at the kidney-exchange network. And in the world of organ transplants, there are no do-overs.

Kerimov and his colleagues have constructed a mathematical model that represents a simplified version of a kidney exchange network.

Within the model, the researchers could dictate which patient-donor pairs could be matched with one another. They can also assign different values to individual matches based on the number of life years they provide. And they can establish the probability that various kinds of patient-donor pairs with particular characteristics might arrive at the network and queue up for a transplant at any given time.

Having set those parameters, the researchers applied different matching policies and compared the results. As it turns out, the answer to whether one should wait or not is: It depends.

To determine which policies generated the best outcomes — i.e., performing matches either daily or periodically — the researchers calculated the difference between the total value in life years that could possibly be generated within the network and the amount generated by a specific policy at a particular point in time. The goal was to keep that number, evocatively dubbed "all-time regret," as small as possible over both the short and long term.

In their first paper, Kerimov and his team explored a complex network in which donor kidneys could be swapped amongst three or more patient-donor pairs. When such multiway matches were possible, the cost of applying a daily-match policy turned out to be onerous. Using all available matches as quickly as possible eliminated the chance of later performing potentially higher-value matches.

Instead, the researchers found they could minimize regret by applying a periodic policy that required waiting for a certain number of patient-donor pairs to arrive before attempting to match them. The model even allowed the team to calculate precisely how long to wait between matchmaking sessions to get the best possible results.

In their second paper, however, the team looked at a simpler network in which kidneys could only be swapped between two donor-patient pairs. Here, their findings contradicted the first: Applying a daily-match policy minimized regret; a periodic matching process yielded no benefit whatsoever.

To their surprise, the researchers discovered they could design a foolproof algorithm for making two-way matches in simple networks. The algorithm employed a ranked list of possible match types; and the researchers found that no matter how many patient-donor pairs of various kinds randomly arrived at the network, the best choice was always simply to perform the highest-ranked match on the list.

In future research, Kerimov hopes to refine the model by feeding it data on real patient-donor pairs that have participated in actual kidney exchange programs. This would allow him to create a more realistic network, more accurately calculate the likelihood that particular kinds of patient-donor pairs will show up, and assign values to matches based not only on life years but also on rarity and difficulty. (Certain blood types and antibody profiles, for example, are rarer or more difficult to match than others.)

But Kerimov already suspects that in a real-world situation, the wisest course of action will be to alternate between periodic and greedy policies as circumstances dictate. In a simple region within a kidney exchange network that only allows for two-way matches, pursuing a greedy policy that involves taking the first match that appears on a fixed menu of options would be the best choice. In a more complex region that allows three-way matches, however, pursuing a periodic matching policy that involves waiting to make rarer and more difficult matches would ultimately offer more patients more years of healthy life.

The benefits of choosing flexibly between greedy and periodic policies should hold for any kind of matching market that can be represented by a network with simpler and more complex regions, such as a logistics system that matches online orders to delivery trucks or a carpooling system that matches passengers with drivers across different parts of a city.

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This article originally ran on Rice Business Wisdom and was based on research from Süleyman Kerimov, an assistant professor of management – operations management in the Jones Graduate School of Business at Rice University.

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VC firm partners with Rice Nexus to open first global office

strategic partnership

Luxembourg-based venture capital and advisory firm MoreThan Capital (MTC) has established its first global office at the new Rice Nexus in Houston’s Ion District as part of a strategic partnership aimed at fostering entrepreneurship and growing Houston as an innovation hub.

MTC has committed to offering its “time, mentorship, industry expertise and global connections” to Rice Nexus. The state-of-the-art Rice Nexus, which opened earlier this year, aims to support and provide resources for ventures that are looking to scale and have "artificial intelligence (AI) as a central pillar of its innovation strategy," according to a statement from Rice.

“The Rice Nexus is a launchpad for world-changing ideas, and this partnership with MoreThan Capital is a key step in realizing that vision,” Sanjoy Paul, executive director of the Rice Nexus, said in a news release. “By combining Rice’s research and entrepreneurial talent with MTC’s global network and mentorship, we are creating an unparalleled engine for innovation that starts in Houston and reaches the world.”

MoreThan Capital has over 100 limited partners, including senior executives and professional investors, based in more than 35 countries.

“Establishing our first global office at the Rice Nexus within the Ion District is a significant milestone for MoreThan Capital,” Guillermo Ruiz, general partner of MoreThan Capital, said in a news release. “We are dedicated to partnering with top-tier academic institutions like Rice University and aligning with organizations that share our core values of trust, engagement and impact.”

The announcement comes just a few weeks after Rice Nexus announced its partnership with Google Public Sector to launch the new Rice AI Venture Accelerator, or RAVA.

This Houston neighbor was the fastest growing U.S. city in last decade

Booming Burb

It's no secret that Houston's population is growing faster than most other metros in the U.S., but now a surprising Houston-area neighbor has been named the No. 1 fastest-growing suburb nationwide over the last decade: the booming city of Fulshear.

Fulshear led the nation with an astonishing 1,082 percent increase in population from 2014 to 2023, according to a recent growth study by marketplace platform StorageCafe.

Overall, Texas cities dominated StorageCafe's list of the top 10 fastest-growing U.S. cities from 2014 to 2023.

The report said the city had nearly 27,000 residents in 2023, but now the U.S. Census Bureau estimates Fulshear's population has now grown to more than 42,600 people.

"With its blend of a relaxed lifestyle, urban conveniences, top-rated schools and strong job opportunities, Fulshear consistently ranks among the best places to live in Texas," the report's author wrote.

This isn't the first time Fulshear has entered the spotlight for its exploding population: it was the No. 2 fastest-growing U.S. city in 2023, and recently came out on top of GoBankingRates' new study ranking of the fastest-growing affluent suburbs in America for 2025.

Several other Houston-area suburbs also saw major growth over the last decade, including Manvel (No. 24), Katy (No. 82), and Conroe (No. 83).

"Manvel doubled its population between 2014 and 2023, while Katy and Conroe each recorded increases of over 50 percent," the report said. "By contrast, Houston itself grew by just 6 percent, aligning with the average growth rate for large U.S. cities."

The report added that the Houston area's population surge has also led to a high demand for housing, where home values have risen 60 percent over the last 10 years. Home prices in Fulshear stood at more than $521,000 in November 2024, whereas Manvel's home prices were over $431,000 during that same period.

For comparison, the national average price of a home is $354,000.

Katy and Conroe had the most affordable home prices out of the four Houston suburbs in the report, at $347,740 and $318,952, respectively, for November.

StorageCafe says the reasons for population shifts vary greatly, with many people seeking out cities with a more affordable cost of living, or those moving for socioeconomic factors like better employment opportunities.

"Population growth is far from even across the U.S. Some cities are experiencing significant increases, directly driven by steady in-migration, rising immigration and birth rates outpacing death rates," the report said. "But what’s fueling these trends runs deeper — economic and social forces like shifting job markets, the rise of remote and hybrid work and soaring living costs are all reshaping where people choose to live."

Other fast-growing Texas cities
Texas had the greatest number of cities to earn spots in the report's ranking of the 100 fastest-growing U.S. cities over the last decade, with 25 total cities making the cut with the highest growth rates nationwide.

Dallas-Fort Worth had the highest number of fastest-growing Texas suburbs on the list, comprising 11 cities: Celina (No. 2), Melissa (No. 3), Princeton (No. 7), Prosper (No. 8), Fate (No. 9), Anna (No. 14), Midlothian (No. 33), Royse City (No. 43), Forney (No. 45), Little Elm (No. 58), and Frisco (No. 72).

Meanwhile, Austin had five suburbs land on the list: Manor (No. 6), Leander (No. 16), Kyle (No. 53), Hutto (No. 54), and Buda (No. 68).

San Antonio also had five suburbs make the top 100, including Boerne (No. 63), Selma (No. 74), Fair Oaks Ranch (No. 70), New Braunfels (No. 77), and Canyon Lake (No. 99).

The top 10 fastest-growing cities over the last decade are:

  • No. 1 – Fulshear, Texas
  • No. 2 – Woodbridge, Virginia
  • No. 3 – Celina, Texas
  • No. 4 – Davenport, Florida
  • No. 5 – Melissa, Texas
  • No. 6 – Manor, Texas
  • No. 7 – Princeton, Texas
  • No. 8 – Prosper, Texas
  • No. 9 – Fate, Texas
  • No. 10 – Nolensville, Tennessee
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This article originally appeared on our sister site, CultureMap.com.

Houston space tech startups share latest updates on lunar missions and more

space update

Houston-based space tech companies Axiom Space and Intuitive Machines recently shared updates on innovative projects and missions, each set to launch by 2027.

Axiom Space

Axiom Space, developer of the world’s first commercial space station and other space infrastructure, is gearing up to launch two orbital data center nodes to low-earth orbit by the end of 2025.

The Axiom Space nodes will lay the foundation for space-based cloud computing. Axiom says orbital data centers provide cloud-enabled data storage and processing, artificial intelligence, and machine learning directly to satellites, constellations, and other spacecraft in Earth’s orbit. This innovation will reduce reliance on earth-based systems, enhance wireless mesh networks and improve real-time operation of space-borne assets, according to Axiom.

Axiom has been working on the development of orbital data centers since 2022. The two nodes going into space in 2025 will be part of Kepler Communications’ 10-satellite data relay network, which is scheduled to launch by the end of this year. Axiom Space and Kepler Communications have been collaborating since 2023.

Kam Ghaffarian, co-founder, executive chairman, and CEO of Axiom, says his company already has deals in place with buyers of space-based cloud computing services. Orbital data centers “are integral to Axiom Space’s vision of era-defining space infrastructure, unlocking transformational capabilities and economic growth,” he says.

Axiom Space says it will be able to buy additional payloads on Kepler’s network to boost capacity for orbital data centers. The two companies will team up to provide network and orbital data center services to various customers.

Intuitive Machines

Meanwhile, Intuitive Machines, a space exploration, infrastructure and services company, has picked SpaceX’s Falcon 9 rocket to launch its fourth delivery mission to the moon. The launch will include two lunar data relay satellites for NASA.

Intuitive Machines says its fourth lunar delivery mission is scheduled for 2027. The mission will comprise six NASA commercial lunar payloads, including a European Space Agency drill set designed to search for water at the moon’s south pole.

“Lunar surface delivery and data relay satellites are central to our strategy to commercialize the moon,” Intuitive Machines CEO Steve Altemus says.

The first of five lunar data relay satellites will be included in the company’s third delivery mission to the moon. The fourth mission, featuring two more satellites, will be followed by two other satellite-delivery missions.