Computers Math

Extremely energy-efficient artificial intelligence is now closer to reality after a study by UCL researchers found a way to improve the accuracy of a brain-inspired computing system.
The system, which uses memristors to create artificial neural networks, is at least 1,000 times more energy efficient than conventional transistor-based AI hardware, but has until now been more prone to error.
Existing AI is extremely energy-intensive — training one AI model can generate 284 tonnes of carbon dioxide, equivalent to the lifetime emissions of five cars. Replacing the transistors that make up all digital devices with memristors, a novel electronic device first built in 2008, could reduce this to a fraction of a tonne of carbon dioxide — equivalent to emissions generated in an afternoon’s drive.
Since memristors are so much more energy-efficient than existing computing systems, they can potentially pack huge amounts of computing power into hand-held devices, removing the need to be connected to the Internet.
This is especially important as over-reliance on the Internet is expected to become problematic in future due to ever-increasing data demands and the difficulties of increasing data transmission capacity past a certain point.
In the new study, published in Nature Communications, engineers at UCL found that accuracy could be greatly improved by getting memristors to work together in several sub-groups of neural networks and averaging their calculations, meaning that flaws in each of the networks could be cancelled out.

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Memristors, described as “resistors with memory,” as they remember the amount of electric charge that flowed through them even after being turned off, were considered revolutionary when they were first built over a decade ago, a “missing link” in electronics to supplement the resistor, capacitor and inductor. They have since been manufactured commercially in memory devices, but the research team say they could be used to develop AI systems within the next three years.
Memristors offer vastly improved efficiency because they operate not just in a binary code of ones and zeros, but at multiple levels between zero and one at the same time, meaning more information can be packed into each bit.
Moreover, memristors are often described as a neuromorphic (brain-inspired) form of computing because, like in the brain, processing and memory are implemented in the same adaptive building blocks, in contrast to current computer systems that waste a lot of energy in data movement.
In the study, Dr Adnan Mehonic, PhD student Dovydas Joksas (both UCL Electronic & Electrical Engineering), and colleagues from the UK and the US tested the new approach in several different types of memristors and found that it improved the accuracy of all of them, regardless of material or particular memristor technology. It also worked for a number of different problems that may affect memristors’ accuracy.
Researchers found that their approach increased the accuracy of the neural networks for typical AI tasks to a comparable level to software tools run on conventional digital hardware.
Dr Mehonic, director of the study, said: “We hoped that there might be more generic approaches that improve not the device-level, but the system-level behaviour, and we believe we found one. Our approach shows that, when it comes to memristors, several heads are better than one. Arranging the neural network into several smaller networks rather than one big network led to greater accuracy overall.”
Dovydas Joksas further explained: “We borrowed a popular technique from computer science and applied it in the context of memristors. And it worked! Using preliminary simulations, we found that even simple averaging could significantly increase the accuracy of memristive neural networks.”
Professor Tony Kenyon (UCL Electronic & Electrical Engineering), a co-author on the study, added: “We believe now is the time for memristors, on which we have been working for several years, to take a leading role in a more energy-sustainable era of IoT devices and edge computing.” More

Just as a living organism continually needs food to maintain itself, an economy consumes energy to do work and keep things going. That consumption comes with the cost of greenhouse gas emissions and climate change, though. So, how can we use energy to keep the economy alive without burning out the planet in the process?
In a paper in PLOS ONE, University of Utah professor of atmospheric sciences Tim Garrett, with mathematician Matheus Grasselli of McMaster University and economist Stephen Keen of University College London, report that current world energy consumption is tied to unchangeable past economic production. And the way out of an ever-increasing rate of carbon emissions may not necessarily be ever-increasing energy efficiency — in fact it may be the opposite.
“How do we achieve a steady-state economy where economic production exists, but does not continually increase our size and add to our energy demands?” Garrett says. “Can we survive only by repairing decay, simultaneously switching existing fossil infrastructure to a non-fossil appetite? Can we forget the flame?”
Thermoeconomics
Garrett is an atmospheric scientist. But he recognizes that atmospheric phenomena, including rising carbon dioxide levels and climate change, are tied to human economic activity. “Since we model the earth system as a physical system,” he says, “I wondered whether we could model economic systems in a similar way.”
He’s not alone in thinking of economic systems in terms of physical laws. There’s a field of study, in fact, called thermoeconomics. Just as thermodynamics describe how heat and entropy (disorder) flow through physical systems, thermoeconomics explores how matter, energy, entropy and information flow through human systems.

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Many of these studies looked at correlations between energy consumption and current production, or gross domestic product. Garrett took a different approach; his concept of an economic system begins with the centuries-old idea of a heat engine. A heat engine consumes energy at high temperatures to do work and emits waste heat. But it only consumes. It doesn’t grow.
Now envision a heat engine that, like an organism, uses energy to do work not just to sustain itself but also to grow. Due to past growth, it requires an ever-increasing amount of energy to maintain itself. For humans, the energy comes from food. Most goes to sustenance and a little to growth. And from childhood to adulthood our appetite grows. We eat more and exhale an ever-increasing amount of carbon dioxide.
“We looked at the economy as a whole to see if similar ideas could apply to describe our collective maintenance and growth,” Garrett says. While societies consume energy to maintain day to day living, a small fraction of consumed energy goes to producing more and growing our civilization.
“We’ve been around for a while,” he adds. “So it is an accumulation of this past production that has led to our current size, and our extraordinary collective energy demands and CO2 emissions today.”
Growth as a symptom
To test this hypothesis, Garrett and his colleagues used economic data from 1980 to 2017 to quantify the relationship between past cumulative economic production and the current rate at which we consume energy. Regardless of the year examined, they found that every trillion inflation-adjusted year 2010 U.S. dollars of economic worldwide production corresponded with an enlarged civilization that required an additional 5.9 gigawatts of power production to sustain itself . In a fossil economy, that’s equivalent to around 10 coal-fired power plants, Garrett says, leading to about 1.5 million tons of CO2 emitted to the atmosphere each year. Our current energy usage, then, is the natural consequence of our cumulative previous economic production.

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They came to two surprising conclusions. First, although improving efficiency through innovation is a hallmark of efforts to reduce energy use and greenhouse gas emissions, efficiency has the side effect of making it easier for civilization to grow and consume more.
Second, that the current rates of world population growth may not be the cause of rising rates of energy consumption, but a symptom of past efficiency gains.
“Advocates of energy efficiency for climate change mitigation may seem to have a reasonable point,” Garrett says, “but their argument only works if civilization maintains a fixed size, which it doesn’t. Instead, an efficient civilization is able to grow faster. It can more effectively use available energy resources to make more of everything, including people. Expansion of civilization accelerates rather than declines, and so do its energy demands and CO2 emissions.”
A steady-state decarbonized future?
So what do those conclusions mean for the future, particularly in relation to climate change? We can’t just stop consuming energy today any more than we can erase the past, Garrett says. “We have inertia. Pull the plug on energy consumption and civilization stops emitting but it also becomes worthless. I don’t think we could accept such starvation.”
But is it possible to undo the economic and technological progress that have brought civilization to this point? Can we, the species who harnessed the power of fire, now “forget the flame,” in Garrett’s words, and decrease efficient growth?
“It seems unlikely that we will forget our prior innovations, unless collapse is imposed upon us by resource depletion and environmental degradation,” he says, “which, obviously, we hope to avoid.”
So what kind of future, then, does Garrett’s work envision? It’s one in which the economy manages to hold at a steady state — where the energy we use is devoted to maintaining our civilization and not expanding it.
It’s also one where the energy of the future can’t be based on fossil fuels. Those have to stay in the ground, he says.
“At current rates of growth, just to maintain carbon dioxide emissions at their current level will require rapidly constructing renewable and nuclear facilities, about one large power plant a day. And somehow it will have to be done without inadvertently supporting economic production as well, in such a way that fossil fuel demands also increase.”
It’s a “peculiar dance,” he says, between eliminating the prior fossil-based innovations that accelerated civilization expansion, while innovating new non-fossil fuel technologies. Even if this steady-state economy were to be implemented immediately, stabilizing CO2 emissions, the pace of global warming would be slowed — not eliminated. Atmospheric levels of CO2 would still reach double their pre-industrial level before equilibrating, the research found.
By looking at the global economy through a thermodynamic lens, Garrett acknowledges that there are unchangeable realities. Any form of an economy or civilization needs energy to do work and survive. The trick is balancing that with the climate consequences.
“Climate change and resource scarcity are defining challenges of this century,” Garrett says. “We will not have a hope of surviving our predicament by ignoring physical laws.”
Future work
This study marks the beginning of the collaboration between Garrett, Grasselli and Keen. They’re now working to connect the results of this study with a full model for the economy, including a systematic investigation of the role of matter and energy in production.
“Tim made us focus on a pretty remarkable empirical relationship between energy consumption and cumulative economic output,” Grasselli says. “We are now busy trying to understand what this means for models that include notions that are more familiar to economists, such as capital, investment and the always important question of monetary value and inflation.” More

In a year defined by obstacles, a University of Illinois at Urbana-Champaign student rocket team persevered. Working together across five time zones, they successfully designed a hybrid rocket engine that uses paraffin and a novel nitrous oxide-oxygen mixture called Nytrox. The team has its sights set on launching a rocket with the new engine at the 2021 Intercollegiate Rocketry and Engineering Competition.
“Hybrid propulsion powers Virgin Galactic’s suborbital tourist spacecraft and the development of that engine has been challenging. Our students are now experiencing those challenges first hand and learning how to overcome them,” said faculty adviser to the team Michael Lembeck.
Last year the team witnessed a number of catastrophic failures with hybrid engines utilizing nitrous oxide. The propellant frequently overheated in the New Mexico desert, where the IREC competition is held. Lembeck said this motivated the team to find an alternative fuel that could remain stable at temperature. Nytrox surfaced as the solution to the problem.
As the team began working on the engine this past spring semester, excitement to conduct hydrostatic testing of the ground oxidizer tank vessel quickly turned to frustration as the team lacked a safe test location.
Team leader Vignesh Sella said, “We planned to conduct the test at the U of I’s Willard airport retired jet engine testing facility. But the Department of Aerospace Engineering halted all testing until safety requirements could be met.”
Sella said they were disheartened at first, but rallied by creating a safety review meeting along with another student rocket group to examine their options.

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“As a result of that meeting, we came up with a plan to move the project forward. The hybrid team rigorously evaluated our safety procedures, and had our work reviewed by Dr. Dassou Nagassou, the Aerodynamics Research Lab manager. He became a great resource for us, and a very helpful mentor.”
Sella and Andrew Larkey also approached Purdue University to draw from their extensive experience in the realm of rocket propulsion. They connected with Chris Nielson who is a graduate student and lab manager at Purdue. They did preliminary over-the-phone design reviews and were eventually invited to conduct their hydrostatic and cold-flow testing at Purdue’s Zucrow Laboratories, a facility dedicated to testing rocket propulsion with several experts in the field on-site.
“We sent a few of the members there to scout the location and take notes before bringing the whole team there for a test,” Sella said. “These meetings, relationships, and advances, although they may sound smooth and easy to establish, were arduous and difficult to attain. It was a great relief to us to have the support from the department, a pressure vessel expert as our mentor, and Zucrow Laboratories available to our team.”
The extended abstract, which the team had submitted much earlier to the AIAA Propulsion and Energy conference, assumed the engine would have been assembled and tested before the documentation process began. Team leader Vignesh Sella said they wanted to document hard test data but had to switch tactics in March. The campus move to online-only classes also curtailed all in-person activities, including those of registered student organizations like ISS.
“As the disruptions caused by COVID-19 required us to work remotely, we pivoted the paper by focusing on documenting the design processes and decisions we made for the engine. This allowed us to work remotely and complete a paper that wasn’t too far from the original abstract. Our members, some of whom are international, met on Zoom and Discord to work on the paper together virtually, over five time zones,” Sella said.

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Sella said he and the entire team are proud of what they have accomplished and are “returning this fall with a vengeance.”
The Illinois Space Society is a technical, professional, and educational outreach student organization at the U of I in the Department of Aerospace Engineering. The society consists of 150 active members. The hybrid rocket engine team consisted of 20 members and is one of the five technical projects within ISS. The project began in 2013 with the goal of constructing a subscale hybrid rocket engine before transitioning to a full-scale engine. The subscale hybrid rocket engine was successfully constructed and hot fired in the summer of 2018, yielding the positive test results necessary to move onto designing and manufacturing a full-scale engine.
“After the engine completes its testing, the next task will be integrating the engine into the rocket vehicle,” said Sella “This will require fitting key flight hardware components within the geometric constraints of a rocket body tube and structurally securing the engine to the vehicle.”
In June 2021, the rocket will be transported to Spaceport America in Truth or Consequences for its first launch.
This work was supported by the U of I Student Sustainability Committee, the Office of Undergraduate Research, and the Illinois Space Society. Technical support was provided by the Department of Aerospace Engineering, the School of Chemical Sciences Machine Shop, Zucrow Laboratories and Christopher D. Nilsen at Purdue University, Stephen A. Whitmore of Utah State University, and Dassou Nagassou of the Aerodynamics Research Laboratory at Illinois. More

Changes to water masses which are stored on the continents can be detected with the help of satellites. The data sets on the Earth’s gravitational field which are required for this, stem from the GRACE and GRACE-FO satellite missions. As these data sets only include the typical large-scale mass anomalies, no conclusions about small scale structures, such as the actual distribution of water masses in rivers and river branches, are possible. Using the South American continent as an example, the Earth system modellers at the German Research Centre for Geosciences GFZ, have developed a new Deep-Learning-Method, which quantifies small as well as large-scale changes to the water storage with the help of satellite data. This new method cleverly combines Deep-Learning, hydrological models and Earth observations from gravimetry and altimetry.
So far it is not precisely known, how much water a continent really stores. The continental water masses are also constantly changing, thus affecting the Earth’s rotation and acting as a link in the water cycle between atmosphere and ocean. Amazon tributaries in Peru, for example, carry huge amounts of water in some years, but only a fraction of it in others. In addition to the water masses of rivers and other bodies of fresh water, considerable amounts of water are also found in soil, snow and underground reservoirs, which are difficult to quantify directly.
Now the research team around primary author Christopher Irrgang developed a new method in order to draw conclusions on the stored water quantities of the South American continent from the coarsely-resolved satellite data. “For the so called down-scaling, we are using a convolutional neural network, in short CNN, in connection with a newly developed training method,” Irrgang says. “CNNs are particularly well suited for processing spatial Earth observations, because they can reliably extract recurrent patterns such as lines, edges or more complex shapes and characteristics.”
In order to learn the connection between continental water storage and the respective satellite observations, the CNN was trained with simulation data of a numerical hydrological model over the period from 2003 until 2018. Additionally, data from the satellite altimetry in the Amazon region was used for validation. What is extraordinary, is that this CNN continuously self-corrects and self-validates in order to make the most accurate statements possible about the distribution of the water storage. “This CNN therefore combines the advantages of numerical modelling with high-precision Earth observation” according to Irrgang.
The researchers’ study shows that the new Deep-Learning-Method is particularly reliable for the tropical regions north of the -20° latitude on the South American continent, where rain forests, vast surface waters and also large groundwater basins are located. Same as for the groundwater-rich, western part of South America’s southern tip. The down-scaling works less well in dry and desert regions. This can be explained by the comparably low variability of the already low water storage there, which therefore only have a marginal effect on the training of the neural network. However, for the Amazon region, the researchers were able to show that the forecast of the validated CNN was more accurate than the numerical model used.
In future, large-scale as well as regional analysis and forecasts of the global continental water storage will be urgently needed. Further development of numerical models and the combination with innovative Deep-Learning-Methods will take up a more important role in this, in order to gain comprehensive insight into continental hydrology. Aside from purely geophysical investigations, there are many other possible applications, such as studying the impact of climate change on continental hydrology, the identification of stress factors for ecosystems such as droughts or floods, and the development of water management strategies for agricultural and urban regions.

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Materials provided by GFZ GeoForschungsZentrum Potsdam, Helmholtz Centre. Note: Content may be edited for style and length. More

One of the biggest impediments to adoption of new technologies is trust in AI.
Now, a new tool developed by USC Viterbi Engineering researchers generates automatic indicators if data and predictions generated by AI algorithms are trustworthy. Their research paper, “There Is Hope After All: Quantifying Opinion and Trustworthiness in Neural Networks” by Mingxi Cheng, Shahin Nazarian and Paul Bogdan of the USC Cyber Physical Systems Group, was featured in Frontiers in Artificial Intelligence.
Neural networks are a type of artificial intelligence that are modeled after the brain and generate predictions. But can the predictions these neural networks generate be trusted? One of the key barriers to adoption of self-driving cars is that the vehicles need to act as independent decision-makers on auto-pilot and quickly decipher and recognize objects on the road — whether an object is a speed bump, an inanimate object, a pet or a child — and make decisions on how to act if another vehicle is swerving towards it. Should the car hit the oncoming vehicle or swerve and hit what the vehicle perceives to be an inanimate object or a child? Can we trust the computer software within the vehicles to make sound decisions within fractions of a second — especially when conflicting information is coming from different sensing modalities such as computer vision from cameras or data from lidar? Knowing which systems to trust and which sensing system is most accurate would be helpful to determine what decisions the autopilot should make.
Lead author Mingxi Cheng was driven to work on this project by this thought: “Even humans can be indecisive in certain decision-making scenarios. In cases involving conflicting information, why can’t machines tell us when they don’t know?”
A tool the authors created named DeepTrust can quantify the amount of uncertainty,” says Paul Bogdan, an associate professor in the Ming Hsieh Department of Electrical and Computer Engineering and corresponding author, and thus, if human intervention is necessary.
Developing this tool took the USC research team almost two years employing what is known as subjective logic to assess the architecture of the neural networks. On one of their test cases, the polls from the 2016 Presidential election, DeepTrust found that the prediction pointing towards Clinton winning had a greater margin for error.
The other significance of this study is that it provides insights on how to test reliability of AI algorithms that are normally trained on thousands to millions of data points. It would be incredibly time-consuming to check if each one of these data points that inform AI predictions were labeled accurately. Rather, more critical, say the researchers, is that the architecture of these neural network systems has greater accuracy. Bogdan notes that if computer scientists want to maximize accuracy and trust simultaneously, this work could also serve as guidepost as to how much “noise” can be in testing samples.
The researchers believe this model is the first of its kind. Says Bogdan, “To our knowledge, there is no trust quantification model or tool for deep learning, artificial intelligence and machine learning. This is the first approach and opens new research directions.” He adds that this tool has the potential to make “artificial intelligence aware and adaptive.”

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Materials provided by University of Southern California. Original written by Amy Blumenthal. Note: Content may be edited for style and length. More

An international team of scientists from the Helmholtz-Zentrum Dresden-Rossendorf (HZDR), the Max Planck Institute for Chemical Physics of Solids, and colleagues from the USA and Switzerland have successfully combined various extreme experimental conditions in a completely unique way, revealing exciting insights into the mysterious conducting properties of the crystalline metal CeRhIn5. In the journal Nature Communications, they report on their exploration of previously uncharted regions of the phase diagram of this metal, which is considered a promising model system for understanding unconventional superconductors.
“First, we apply a thin layer of gold to a microscopically small single crystal. Then we use an ion beam to carve out tiny microstructures. At the ends of these structures, we attach ultra-thin platinum tapes to measure resistance along different directions under extremely high pressures, which we generate with a diamond anvil pressure cell. In addition, we apply very powerful magnetic fields to the sample at temperatures near absolute zero.”
To the average person, this may sound like an overzealous physicist’s whimsical fancy, but in fact, it is an actual description of the experimental work conducted by Dr. Toni Helm from HZDR’s High Magnetic Field Laboratory (HLD) and his colleagues from Tallahassee, Los Alamos, Lausanne and Dresden. Well, at least in part, because this description only hints at the many challenges involved in combining such extremes concurrently. This great effort is, of course, not an end in itself: the researchers are trying to get to the bottom of some fundamental questions of solid state physics.
The sample studied is cer-rhodium-indium-five (CeRhIn5), a metal with surprising properties that are not fully understood yet. Scientists describe it as an unconventional electrical conductor with extremely heavy charge carriers, in which, under certain conditions, electrical current can flow without losses. It is assumed that the key to this superconductivity lies in the metal’s magnetic properties. The central issues investigated by physicists working with such correlated electron systems include: How do heavy electrons organize collectively? How can this cause magnetism and superconductivity? And what is the relationship between these physical phenomena?
An expedition through the phase diagram
The physicists are particularly interested in the metal’s phase diagram, a kind of map whose coordinates are pressure, magnetic field strength, and temperature. If the map is to be meaningful, the scientists have to uncover as many locations as possible in this system of coordinates, just like a cartographer exploring unknown territory. In fact, the emerging diagram is not unlike the terrain of a landscape.
As they reduce temperature to almost four degrees above absolute zero, the physicists observe magnetic order in the metal sample. At this point, they have a number of options: They can cool the sample down even further and expose it to high pressures, forcing a transition into the superconducting state. If, on the other hand, they solely increase the external magnetic field to 600,000 times the strength of the earth’s magnetic field, the magnetic order is also suppressed; however, the material enters a state called “electronically nematic.”
This term is borrowed from the physics of liquid crystals, where it describes a certain spatial orientation of molecules with a long-range order over larger areas. The scientists assume that the electronically nematic state is closely linked to the phenomenon of unconventional superconductivity. The experimental environment at HLD provides optimum conditions for such a complex measurement project. The large magnets generate relatively long-lasting pulses and offer sufficient space for complex measurement methods under extreme conditions.
Experiments at the limit afford a glimpse of the future
The experiments have a few additional special characteristics. For example, working with high-pulsed magnetic fields creates eddy currents in the metallic parts of the experimental setup, which can generate unwanted heat. The scientists have therefore manufactured the central components from a special plastic material that suppresses this effect and functions reliably near absolute zero. Through the microfabrication by focused ion beams, they produce a sample geometry that guarantees a high-quality measurement signal.
“Microstructuring will become much more important in future experiments. That’s why we brought this technology into the laboratory right away,” says Toni Helm, adding: “So we now have ways to access and gradually penetrate into dimensions where quantum mechanical effects play a major role.” He is also certain that the know-how he and his team have acquired will contribute to research on high-temperature superconductors or novel quantum technologies.

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Materials provided by Helmholtz-Zentrum Dresden-Rossendorf. Original written by Dr. Bernd Schröder. Note: Content may be edited for style and length. More

Photonic integrated circuits that use light instead of electricity for computing and signal processing promise greater speed, increased bandwidth, and greater energy efficiency than traditional circuits using electricity.
But they’re not yet small enough to compete in computing and other applications where electric circuits continue to reign.
Electrical engineers at the University of Rochester believe they’ve taken a major step in addressing the problem. Using a material widely adopted by photonics researchers, the Rochester team has created the smallest electro-optical modulator yet. The modulator is a key component of a photonics-based chip, controlling how light moves through its circuits.
In Nature Communications, the lab of Qiang Lin, professor of electrical and computer engineering, describes using a thin film of lithium niobate (LN) bonded on a silicon dioxide layer to create not only the smallest LN modulator yet, but also one that operates at high speed and is energy efficient.
This “paves a crucial foundation for realizing large-scale LN photonic integrated circuits that are of immense importance for broad applications in data communication, microwave photonics, and quantum photonics,” writes lead author Mingxiao Li, a graduate student in Lin’s lab.
Because of its outstanding electro-optic and nonlinear optic properties, lithium niobate has “become a workhorse material system for photonics research and development,” Lin says. “However current LN photonic devices, made upon either bulk crystal or thin-film platform require large dimensions and are difficult to scale down in size, which limits the modulation efficiency, energy consumption, and the degree of circuit integration. A major challenge lies in making high-quality nanoscopic photonic structures with high precision.”
The modulator project builds upon the lab’s previous use of lithium niobate to create a photonic nanocavity — another key component in photonic chips. At only about a micron in size, the nanocavity can tune wavelengths using only two to three photons at room temperature — “the first time we know of that even two or three photons have been manipulated in this way at room temperatures,” Lin says. That device was described in a paper in Optica.
The modulator could be used in conjunction with a nanocavity in creating a photonic chip at the nanoscale.
The project was supported with funding from the National Science Foundation, Defense Threat Reduction Agency, and Defense Advanced Research Projects Agency (DARPA); fabrication of the device was done in part at the Cornell NanoScale Facility.

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Materials provided by University of Rochester. Original written by Bob Marcotte. Note: Content may be edited for style and length. More

Male lions typically have manes. Male peacocks have six-foot-long tail feathers. Female eagles and hawks can be about 30% bigger than males. But if you only had these animals’ fossils to go off of, it would be hard to confidently say that those differences were because of the animals’ sex. That’s the problem that paleontologists face: it’s hard to tell if dinosaurs with different features were separate species, different ages, males and females of the same species, or just varied in a way that had nothing to do with sex. A lot of the work trying to show differences between male and female dinosaurs has come back inconclusive. But in a new paper, scientists show how using a different kind of statistical analysis can often estimate the degree of sexual variation in a dataset of fossils.
“It’s a whole new way of looking at fossils and judging the likelihood that the traits we see correlate with sex,” says Evan Saitta, a research associate at Chicago’s Field Museum and the lead author of the new paper in the Biological Journal of the Linnean Society. “This paper is part of a larger revolution of sorts about how to use statistics in science, but applied in the context of paleontology.”
Unless you find a dinosaur skeleton that contains the fossilized eggs that it was about to lay, or a similar dead giveaway, it’s hard to be sure about an individual dinosaur’s sex. But many birds, the only living dinosaurs, vary a lot between males and females on average, a phenomenon called sexual dimorphism. Dinosaurs’ cousins, the crocodilians, show sexual dimorphism too. So it stands to reason that in many species of dinosaurs, males and females would differ from each other in a variety of traits.
But not all differences in animals of the same species are linked to their sex. For example, in humans, average height is related to sex, but other traits like eye color and hair color don’t neatly map onto men versus women. We often don’t know precisely how the traits we see in dinosaurs relate to their sex, either. Since we don’t know if, say, larger dinosaurs were female, or dinosaurs with bigger crests on their heads were male, Saitta and his colleagues looked for patterns in the differences between individuals of the same species. To do that, they examined measurements from a bunch of fossils and modern species and did a lot of math.
Other paleontologists have tried to look for sexual dimorphism in dinosaurs using a form of statistics (called significance testing, for all you stats nerds) where you collect all your data points and then calculate the probability that those results could have happened by pure chance rather than an actual cause (like how doctors determine whether a new medicine is more helpful than a placebo). This kind of analysis sometimes works for big, clean datasets. But, says Saitta, “with a lot of these dinosaur tests, our data is pretty bad” — there aren’t that many fossil specimens, or they’re incomplete or poorly preserved. Using significance testing in these cases, Saitta argues, results in a lot of false negatives: since the samples are small, it takes an extreme amount of variation between the sexes to trigger a positive test result. (Significance testing isn’t just a consideration for paleontologists — concerns over a “replication crisis” have plagued researchers in psychology and medicine, where certain studies are difficult to reproduce.)
Instead, Saitta and his colleagues experimented with another form of stats, called effect size statistics. Effect size statistics is better for smaller datasets because it attempts to estimate the degree of sex differences and calculate the uncertainty in that estimate. This alternative statistical method takes natural variations into account without viewing dimorphism as black-or-white-many sexual dimorphisms can be subtle. Co-author Max Stockdale of the University of Bristol wrote the code to run the statistical simulations. Saitta and his colleagues uploaded measurements of dinosaur fossils to the program, and it yielded estimates of body mass dimorphism and error bars in those estimates that would have simply been dismissed using significance testing.
“We showed that if you adopt this paradigm shift in statistics, where you attempt to estimate the magnitude of an effect and then put error bars around that, you can often produce a fairly accurate estimate of sexual variation even when the sexes of the individuals are unknown,” says Saitta.
For instance, Saitta and his colleagues found that in the dinosaur Maiasaura, adult specimens vary a lot in size, and the analyses show that these are likelier to correspond to sexual variation than differences seen in other dinosaur species. But while the current data suggest that one sex was about 45% bigger than the other, they can’t tell if the bigger ones are males or females.
While there’s a lot of work yet to be done, Saitta says he’s excited that the statistical simulations gave such consistent results despite the limits of the fossil data.
“Sexual selection is such an important driver of evolution, and to limit ourselves to ineffective statistical approaches hurts our ability to understand the paleobiology of these animals,” he says. “We need to account for sexual variation in the fossil record.”
“I’m happy to play a small part in this sort of statistical revolution,” he adds. “Effect size statistics has a major impact for psychological and medical research, so to apply it to dinosaurs and paleontology is really cool.”

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Materials provided by Field Museum. Note: Content may be edited for style and length. More