Computers Math

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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Turing machines were first proposed by British mathematician Alan Turing in 1936, and are a theoretical mathematical model of what it means for a system to “be a computer.”
At a high level, these machines are similar to real-world modern computers because they have storage for digital data and programs (somewhat like a hard drive), a little central processing unit (CPU) to perform computations, and can read programs from their storage, run them, and produce outputs. Amazingly, Turing proposed his model before real-world electronic computers existed.
In a paper published in the American Physical Society’s Physical Review Research, Santa Fe Institute researchers Artemy Kolchinsky and David Wolpert present their work exploring the thermodynamics of computation within the context of Turing machines.
“Our hunch was that the physics of Turing machines would show a lot of rich and novel structure because they have special properties that simpler models of computation lack, such as universality,” says Kolchinsky.
Turing machines are widely believed to be universal, in the sense that any computation done by any system can also be done by a Turing machine.
The quest to find the cost of running a Turing machine began with Wolpert trying to use information theory — the quantification, storage, and communication of information — to formalize how complex a given operation of a computer is. While not restricting his attention to Turing machines per se, it was clear that any results he derived would have to apply to them as well.
During the process, Wolpert stumbled onto the field of stochastic thermodynamics. “I realized, very grudgingly, that I had to throw out the work I had done trying to reformulate nonequilibrium statistical physics, and instead adopt stochastic thermodynamics,” he says. “Once I did that, I had the tools to address my original question by rephrasing it as: In terms of stochastic thermodynamics cost functions, what’s the cost of running a Turing machine? In other words, I reformulated my question as a thermodynamics of computation calculation.”
Thermodynamics of computation is a subfield of physics that explores what the fundamental laws of physics say about the relationship between energy and computation. It has important implications for the absolute minimum amount of energy required to perform computations.
Wolpert and Kolchinsky’s work shows that relationships exist between energy and computation that can be stated in terms of algorithmic information (which defines information as compression length), rather than “Shannon information” (which defines information as reduction of uncertainty about the state of the computer).
Put another way: The energy required by a computation depends on how much more compressible the output of the computation is than the input. “To stretch a Shakespeare analogy, imagine a Turing machine reads-in the entire works of Shakespeare, and then outputs a single sonnet,” explains Kolchinsky. “The output has a much shorter compression than the input. Any physical process that carries out that computation would, relatively speaking, require a lot of energy.”
While important earlier work also proposed relationships between algorithmic information and energy, Wolpert and Kolchinsky derived these relationships using the formal tools of modern statistical physics. This allows them to analyze a broader range of scenarios and to be more precise about the conditions under which their results hold than was possible by earlier researchers.
“Our results point to new kinds of relationships between energy and computation,” says Kolchinsky. “This broadens our understanding of the connection between contemporary physics and information, which is one of the most exciting research areas in physics.”

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New research shows that U.S. political parties are becoming increasingly polarized due to their quest for voters — not because voters themselves are becoming more extremist.
The research team, which includes Northwestern University researchers, found that extremism is a strategy that has worked over the years even if voters’ views remain in the center. Voters are not looking for a perfect representative but a “satisficing,” meaning “good enough,” candidate.
“Our assumption is not that people aren’t trying to make the perfect choice, but in the presence of uncertainty, misinformation or a lack of information, voters move toward satisficing,” said Northwestern’s Daniel Abrams, a senior author of the study.
The study is now available online and will be published in SIAM Review’s printed edition on Sept. 1.
Abrams is an associate professor of engineering sciences and applied mathematics in Northwestern’s McCormick School of Engineering. Co-authors include Adilson Motter, the Morrison Professor of Physics and Astronomy in Northwestern’s Weinberg College of Arts and Sciences, and Vicky Chuqiao Yang, a postdoctoral fellow at the Santa Fe Institute and former student in Abrams’ laboratory.
To accommodate voters’ “satisficing” behavior, the team developed a mathematical model using differential equations to understand how a rational political party would position itself to get the most votes. The tool is reactive, with the past influencing future behaviors of the parties.

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The team tested 150 years of U.S. Congressional voting data and found the model’s predictions are consistent with the political parties’ historical trajectories: Congressional voting has shifted to the margins, but voters’ positions have not changed much.
“The two major political parties have been getting more and more polarized since World War II, while historical data indicates the average American voter remains just as moderate on key issues and policies as they always have been,” Abrams said.
The team found that polarization is instead tied to the ideological homogeneity within the constituencies of the two major parties. To differentiate themselves, the politicians of the parties move further away from the center.
The new model helps explains why. The moves to the extremes can be interpreted as attempts by the Democratic and Republican parties to minimize an overlap of constituency. Test runs of the model show how staying within the party lines creates a winning strategy.
“Right now, we have one party with a lot of support from minorities and women, and another party with a lot of support from white men,” Motter said.

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Why not have both parties appeal to everyone? “Because of the perception that if you gain support from one group, it comes at the expense of the other group,” he added. “The model shows that the increased polarization is not voters’ fault. It is a way to get votes. This study shows that we don’t need to assume that voters have a hidden agenda driving polarization in Congress. There is no mastermind behind the policy. It is an emergent phenomenon.”
The researchers caution that many other factors — political contributions, gerrymandering and party primaries — also contribute to election outcomes, which future work can examine.
The work challenges a model introduced in the late 1950s by economist Anthony Downs, which assumes everyone votes and makes well-informed, completely rational choices, picking the candidate closest to their opinions. The Downsian model predicts that political parties over time would move closer to the center.
However, U.S. voters’ behaviors don’t necessarily follow those patterns, and the parties’ positions have become dramatically polarized.
“People aren’t perfectly rational, but they’re not totally irrational either,” Abrams said. “They’ll vote for the candidate that’s good enough — or not too bad — without making fine distinctions among those that meet their perhaps low bar for good enough. If we want to reduce political polarization between the parties, we need both parties to be more tolerant of the diversity within their own ranks.” More