Computers Math

Scientists using one of the world’s most powerful quantum microscopes have made a discovery that could have significant consequences for the future of computing.
Researchers at the Macroscopic Quantum Matter Group laboratory in University College Cork (UCC) have discovered a spatially modulating superconducting state in a new and unusual superconductor Uranium Ditelluride (UTe2). This new superconductor may provide a solution to one of quantum computing’s greatest challenges.
Their finding has been published in the  journal Nature.
Lead author Joe Carroll, a PhD researcher working with UCC Prof. of Quantum Physics Séamus Davis, explains the subject of the paper.
“Superconductors are amazing materials which have many strange and unusual properties. Most famously they allow electricity to flow with zero resistance. That is, if you pass a current through them they don’t start to heat up, in fact, they don’t dissipate any energy despite carrying a huge current. They can do this because instead of individual electrons moving through the metal we have pairs of electrons which bind together. These pairs of electrons together form macroscopic quantum mechanical fluid.”
“What our team found was that some of the electron pairs form a new crystal structure embedded in this background fluid. These types of states were first discovered by our group in 2016 and are now called Electron Pair-Density Waves. These Pair Density Waves are a new form of superconducting matter the properties of which we are still discovering.”
“What is particularly exciting for us and the wider community is that UTe2 appears to be a new type of superconductor. Physicists have been searching for a material like it for nearly 40 years. The pairs of electrons appear to have intrinsic angular momentum. If this is true, then what we have detected is the first Pair-Density Wave composed of these exotic pairs of electrons.”

When asked about the practical implications of this work Mr. Carroll explained:
“There are indications that UTe2 is a special type of superconductor that could have huge consequences for quantum computing.”
“Typical, classical, computers use bits to store and manipulate information. Quantum computers rely on quantum bits or qubits to do the same. The problem facing existing quantum computers is that each qubit must be in a superposition with two different energies — just as Schrödinger’s cat could be called both ‘dead’ and ‘alive’. This quantum state is very easily destroyed by collapsing into the lowest energy state — ‘dead’ — thereby cutting off any useful computation.
“This places huge limits on the application of quantum computers. However, since its discovery five years ago there has been a huge amount of research on UTe2 with evidence pointing to it being a superconductor which may be used as a basis for topological quantum computing. In such materials there is no limit on the lifetime of the qubit during computation opening up many new ways for more stable and useful quantum computers. In fact, Microsoft have already invested billions of dollars into topological quantum computing so this is a well-established theoretical science already.” he said.
“What the community has been searching for is a relevant topological superconductor; UTe2 appears to be that.”
“What we’ve discovered then provides another piece to the puzzle of UTe2. To make applications using materials like this we must understand their fundamental superconducting properties. All of modern science moves step by step. We are delighted to have contributed to the understanding of a material which could bring us closer to much more practical quantum computers.”
Congratulating the research team at the Macroscopic Quantum Matter Group Laboratory in University College Cork, Professor John F. Cryan, Vice President Research and Innovation said:
“This important discovery will have significant consequences for the future of quantum computing. In the coming weeks, the University will launch UCC Futures — Future Quantum and Photonics and research led by Professor Seamus Davis and the Macroscopic Quantum Matter Group, with the use of one of the world’s most powerful microscopes, will play a crucial role in this exciting initiative.” More

A research group at the Graduate School of Science, Nagoya University in Japan has used artificial intelligence to determine that Piezo, a channel that receives mechanical stimuli, plays a role in controlling the mating posture of male fruit flies (Drosophila melanogaster). Inhibition of Piezo led the flies to adopt an ineffective mating posture that decreased their reproductive performance. Their findings were reported in iScience.
Most previous studies of animal mating have been limited to behavioral studies, limiting our understanding of this essential process. Since many animals adopt a fixed posture during copulation, maintaining an effective mating position is vital for reproductive success. In fruit flies, the male mounts the female and maintains this posture for at least until he transfers sufficient sperm to fertilize the female, which occurs about 8 minutes after copulation initiation. The Nagoya University research group realized that some factor was involved in maintaining this copulation posture.
A likely contender is Piezo. Piezo is a family of transmembrane proteins found in bristle cells, the sensitive cells in male genitals. Piezo is activated when a mechanical force is applied to a cell membrane, allowing ions to flow through the channel and generate an electrical signal. This signal triggers cellular responses, including the release of neurotransmitters in neurons and the contraction of muscle cells. Such feedback helps a fly maintain his mating position.
After identifying that the piezo gene is involved in the mating of fruit flies, Professor Azusa Kamikouchi (she/her), Assistant Professor Ryoya Tanaka (he/him), and student Hayato M. Yamanouchi (he/him) used optogenetics to further explore the neural mechanism of this phenomenon. This technique combines genetic engineering and optical science to create genetically modified neurons that can be inactivated with light of specific wavelengths. When the light was turned on during mating, the neuron was silenced. This allowed the researchers to manipulate the activity of piezo-expressing neurons.
“This step proved to be a big challenge for us,” Kamikouchi said. “Using optogenetics, specific neurons are silenced only when exposed to photostimulation. However, our interest was silencing neural activity during copulation. Therefore, we had to make sure that the light was only turned on during mating. However, if the experimenter manually turned the photostimulation on in response to the animal’s copulation, they needed to observe the animal throughout the experiment. Waiting around for fruit flies to mate is incredibly time-consuming.”
The observation problem led the group to establish an experimental deep learning system that could recognize copulation. By training the AI to recognize when sexual intercourse was occurring, they could automatically control photostimulation. This allowed them to discover that when piezo-expressing neurons were inhibited, males adopted a wonky, largely ineffective mating posture. As one might expect, the males that showed difficulty in adopting an appropriate sexual position had fewer offspring. They concluded that a key role of the piezo gene was helping the male shift his axis in response to the female for maximum mating success.
“Piezo proteins have been implicated in a variety of physiological processes, including touch sensation, hearing, blood pressure regulation, and bladder function,” said Kamikouchi. “Now our findings suggest that reproduction can be added to the list. Since mating is an important behavior for reproduction that is widely conserved in animals, understanding its control mechanism will lead to a greater understanding of the reproductive system of animals in general.”
Kamikouchi is enthusiastic about the use of AI in such research. “With the recent development of informatics, experimental systems and analysis methods have advanced dramatically,” she concludes. “In this research, we have succeeded in creating a device that automatically detects mating using machine learning-based real-time analysis and controls photostimulation necessary for optogenetics. To investigate the neural mechanisms that control animal behavior, it is important to conduct experiments in which neural activity is manipulated only when an individual exhibits a specific behavior. The method established in this study can be applied not only to the study of mating in fruit flies but also to various behaviors in other animals. It should make a significant contribution to the promotion of neurobiological research.” More

Measuring human brain activity down to the cellular level: until now, this has been possible only to a limited extent. With a new approach developed by researchers at the Technical University of Munich (TUM), it will now be much easier. The method relies on microelectrodes along with the support of brain tumor patients, who participate in studies while undergoing “awake” brain surgery. This enabled the team to identify how our brain processes numbers.
We use numbers every day. It happens in a very concrete way when we count objects. And it happens abstractly, for example when we see the symbol “8” or do complex calculations.
In a study published in the journal Cell Reports, a team of researchers and clinicians working with Simon Jacob, Professor of Translational Neurotechnology at the Department of Neurosurgery at TUM’s university hospital Klinikum rechts der Isar, was able to show how the brain processes numbers. The researchers found that individual neurons in the brains of participants were specialized in handling specific numbers. Each one of these neurons was particularly active when its “preferred” number of elements in a dot pattern was presented to the patient. To a somewhat lesser degree this was also the case when the subjects processed number symbols.
“We already knew that animals processed numbers of objects in this way,” says Prof. Jacob. “But until now, it was not possible to demonstrate conclusively how it works in humans. This has brought us a step closer to unravelling the mechanisms of cognitive functions and developing solutions when things go wrong with these brain functions, for example.”
Recording individual neurons is a challenge
To get to this result, Prof. Jacob and his team first had to solve a fundamental problem. “The brain functions by means of electrical impulses,” says Simon Jacob. “So it is by detecting these signals directly that we can learn the most about cognition and perception.”
There are, however, few opportunities for direct measurements of human brain activity. Neurons cannot be individually recorded through the skull. Some medical teams surgically implant electrodes in epilepsy patients. However, these procedures do not reach the brain region believed to be responsible for processing numbers.

Innovative advancement of established approaches
Simon Jacob and an interdisciplinary team therefore developed an approach that adapts established technologies and opens up entirely new possibilities in neuroscience. At the heart of the procedure are microelectrode arrays that have undergone extensive testing in animal studies.
To ensure that the electrodes would produce reliable data in awake surgeries on the human brain, the researchers had to reconfigure them in close collaboration with the manufacturer. The trick was to increase the distance between the needle-like sensors used to record the electrical activities of a cell. “In theory, tightly packed electrodes will produce more data,” says Simon Jacob. “But in practice the large number of contacts stuns the implanted brain region, so that no usable data are recorded.”
Patients support research
The development of the procedure was possible only because patients with brain tumors agreed to support the research team. While undergoing brain surgery, they permitted sensors to be implanted and performed test tasks for the researchers. According to Simon Jacob, the experimental procedures did not negatively affect the work of the surgical team.
A greater number of medical centers can conduct studies
“Our procedure has two key advantages,” says Simon Jacob. First, such tumor surgeries provide access to a much larger area of the brain. “And second, with the electrodes we used, which have been standardized and tested in years of animal trials, many more medical centers will be able to measure neuronal activity in the future” says Jacob. While epilepsy operations are performed only at a small number of centers and on relatively few patients, he explains, many more university hospitals perform awake operations on patients with brain tumors. “With a significantly larger number of studies with standardized methods and sensors, we can learn a lot more in the coming years about how the human brain functions,” says Simon Jacob. More

Picture a network of interconnected, autonomous robots working together in a coordinated dance to navigate the pitch-black surroundings of the ocean while carrying out scientific surveys or search-and-rescue missions.
In a new study published in Scientific Reports, a team led by Brown University researchers has presented important first steps in building these types of underwater navigation robots. In the study, the researchers outline the design of a small robotic platform called Pleobot that can serve as both a tool to help researchers understand the krill-like swimming method and as a foundation for building small, highly maneuverable underwater robots.
Pleobot is currently made of three articulated sections that replicate krill-like swimming called metachronal swimming. To design Pleobot, the researchers took inspiration from krill, which are remarkable aquatic athletes and display mastery in swimming, accelerating, braking and turning. They demonstrate in the study the capabilities of Pleobot to emulate the legs of swimming krill and provide new insights on the fluid-structure interactions needed to sustain steady forward swimming in krill.
According to the study, Pleobot has the potential to allow the scientific community to understand how to take advantage of 100 million years of evolution to engineer better robots for ocean navigation.
“Experiments with organisms are challenging and unpredictable,” said Sara Oliveira Santos, a Ph.D. candidate at Brown’s School of Engineering and lead author of the new study. “Pleobot allows us unparalleled resolution and control to investigate all the aspects of krill-like swimming that help it excel at maneuvering underwater. Our goal was to design a comprehensive tool to understand krill-like swimming, which meant including all the details that make krill such athletic swimmers.”
The effort is a collaboration between Brown researchers in the lab of Assistant Professor of Engineering Monica Martinez Wilhelmus and scientists in the lab of Francisco Cuenca-Jimenez at the Universidad Nacional Autónoma de México.

A major aim of the project is to understand how metachronal swimmers, like krill, manage to function in complex marine environments and perform massive vertical migrations of over 1,000 meters — equivalent to stacking three Empire State Buildings — twice daily.
“We have snapshots of the mechanisms they use to swim efficiently, but we do not have comprehensive data,” said Nils Tack, a postdoctoral associate in the Wilhelmus lab. “We built and programmed a robot that precisely emulates the essential movements of the legs to produce specific motions and change the shape of the appendages. This allows us to study different configurations to take measurements and make comparisons that are otherwise unobtainable with live animals.”
The metachronal swimming technique can lead to remarkable maneuverability that krill frequently display through the sequential deployment of their swimming legs in a back to front wave-like motion. The researchers believe that in the future, deployable swarm systems can be used to map Earth’s oceans, participate in search-and-recovery missions by covering large areas, or be sent to moons in the solar system, such as Europa, to explore their oceans.
“Krill aggregations are an excellent example of swarms in nature: they are composed of organisms with a streamlined body, traveling up to one kilometer each way, with excellent underwater maneuverability,” Wilhelmus said. “This study is the starting point of our long-term research aim of developing the next generation of autonomous underwater sensing vehicles. Being able to understand fluid-structure interactions at the appendage level will allow us to make informed decisions about future designs.”
The researchers can actively control the two leg segments and have passive control of Pleobot’s biramous fins. This is believed to be the first platform that replicates the opening and closing motion of these fins. The construction of the robotic platform was a multi-year project, involving a multi-disciplinary team in fluid mechanics, biology and mechatronics.

The researchers built their model at 10 times the scale of krill, which are usually about the size of a paperclip. The platform is primarily made of 3D printable parts and the design is open-access, allowing other teams to use Pleobot to continue answering questions on metachronal swimming not just for krill but for other organisms like lobsters.
In the published study, the group reveals the answer to one of the many unknown mechanisms of krill swimming: how they generate lift in order not to sink while swimming forward. If krill are not swimming constantly, they will start sinking because they are a little heavier than water. To avoid this, they still have to create some lift even while swimming forward to be able to remain at that same height in the water, said Oliveira Santos.
“We were able to uncover that mechanism by using the robot,” said Yunxing Su, a postdoctoral associate in the lab. “We identified an important effect of a low-pressure region at the back side of the swimming legs that contributes to the lift force enhancement during the power stroke of the moving legs.”
In the coming years, the researchers hope to build on this initial success and further build and test the designs presented in the article. The team is currently working to integrate morphological characteristics of shrimp into the robotic platform, such as flexibility and bristles around the appendages.
The work was partially funded by a NASA Rhode Island EPSCoR Seed Grant. More

Quantum computing could revolutionize our world. For specific and crucial tasks, it promises to be exponentially faster than the zero-or-one binary technology that underlies today’s machines, from supercomputers in laboratories to smartphones in our pockets. But developing quantum computers hinges on building a stable network of qubits — or quantum bits — to store information, access it and perform computations.
Yet the qubit platforms unveiled to date have a common problem: They tend to be delicate and vulnerable to outside disturbances. Even a stray photon can cause trouble. Developing fault-tolerant qubits — which would be immune to external perturbations — could be the ultimate solution to this challenge.
A team led by scientists and engineers at the University of Washington has announced a significant advancement in this quest. In a pair of papers published June 14 in Nature and June 22 in Science, they report that, in experiments with flakes of semiconductor materials — each only a single layer of atoms thick — they detected signatures of “fractional quantum anomalous Hall” (FQAH) states. The team’s discoveries mark a first and promising step in constructing a type of fault-tolerant qubit because FQAH states can host anyons — strange “quasiparticles” that have only a fraction of an electron’s charge. Some types of anyons can be used to make what are called “topologically protected” qubits, which are stable against any small, local disturbances.
“This really establishes a new paradigm for studying quantum physics with fractional excitations in the future,” said Xiaodong Xu, the lead researcher behind these discoveries, who is also the Boeing Distinguished Professor of Physics and a professor of materials science and engineering at the UW.
FQAH states are related to the fractional quantum Hall state, an exotic phase of matter that exists in two-dimensional systems. In these states, electrical conductivity is constrained to precise fractions of a constant known as the conductance quantum. But fractional quantum Hall systems typically require massive magnetic fields to keep them stable, making them impractical for applications in quantum computing. The FQAH state has no such requirement — it is stable even “at zero magnetic field,” according to the team.
Hosting such an exotic phase of matter required the researchers to build an artificial lattice with exotic properties. They stacked two atomically thin flakes of the semiconductor material molybdenum ditelluride (MoTe2) at small, mutual “twist” angles relative to one another. This configuration formed a synthetic “honeycomb lattice” for electrons. When researchers cooled the stacked slices to a few degrees above absolute zero, an intrinsic magnetism arose in the system. The intrinsic magnetism takes the place of the strong magnetic field typically required for the fractional quantum Hall state. Using lasers as probes, the researchers detected signatures of the FQAH effect, a major step forward in unlocking the power of anyons for quantum computing.

The team — which also includes scientists at the University of Hong Kong, the National Institute for Materials Science in Japan, Boston College and the Massachusetts Institute of Technology — envisions their system as a powerful platform to develop a deeper understanding of anyons, which have very different properties from everyday particles like electrons. Anyons are quasiparticles — or particle-like “excitations” — that can act as fractions of an electron. In future work with their experimental system, the researchers hope to discover an even more exotic version of this type of quasiparticle: “non-Abelian” anyons, which could be used as topological qubits. Wrapping — or “braiding” — the non-Abelian anyons around each other can generate an entangled quantum state. In this quantum state, information is essentially “spread out” over the entire system and resistant to local disturbances — forming the basis of topological qubits and a major advancement over the capabilities of current quantum computers.
“This type of topological qubit would be fundamentally different from those that can be created now,” said UW physics doctoral student Eric Anderson, who is lead author of the Science paper and co-lead author of the Nature paper. “The strange behavior of non-Abelian anyons would make them much more robust as a quantum computing platform.”
Three key properties, all of which existed simultaneously in the researchers’ experimental setup, allowed FQAH states to emerge: Magnetism: Though MoTe2 is not a magnetic material, when they loaded the system with positive charges, a “spontaneous spin order” — a form of magnetism called ferromagnetism — emerged. Topology: Electrical charges within their system have “twisted bands,” similar to a Möbius strip, which helps make the system topological. Interactions: The charges within their experimental system interact strongly enough to stabilize the FQAH state.The team hopes that, using their approach, non-Abelian anyons await for discovery.
“The observed signatures of the fractional quantum anomalous Hall effect are inspiring,” said UW physics doctoral student Jiaqi Cai, co-lead author on the Nature paper and co-author of the Science paper. “The fruitful quantum states in the system can be a laboratory-on-a-chip for discovering new physics in two dimensions, and also new devices for quantum applications.”
“Our work provides clear evidence of the long-sought FQAH states,” said Xu, who is also a member of the Molecular Engineering and Sciences Institute, the Institute for Nano-Engineered Systems and the Clean Energy Institute, all at UW. “We are currently working on electrical transport measurements, which could provide direct and unambiguous evidence of fractional excitations at zero magnetic field.”
The team believes that, with their approach, investigating and manipulating these unusual FQAH states can become commonplace — accelerating the quantum computing journey.
Additional co-authors on the papers are William Holtzmann and Yinong Zhang in the UW Department of Physics; Di Xiao, Chong Wang, Xiaowei Zhang, Xiaoyu Liu and Ting Cao in the UW Department of Materials Science & Engineering; Feng-Ren Fan and Wang Yao at the University of Hong Kong and the Joint Institute of Theoretical and Computational Physics at Hong Kong; Takashi Taniguchi and Kenji Watanabe from the National Institute of Materials Science in Japan; Ying Ran of Boston College; and Liang Fu at MIT. The research was funded by the U.S. Department of Energy, the Air Force Office of Scientific Research, the National Science Foundation, the Research Grants Council of Hong Kong, the Croucher Foundation, the Tencent Foundation, the Japan Society for the Promotion of Science and the University of Washington. More

Computer scientists at the University of Waterloo have discovered a method of attack that can successfully bypass voice authentication security systems with up to a 99% success rate after only six tries.
Voice authentication — which allows companies to verify the identity of their clients via a supposedly unique “voiceprint” — has increasingly been used in remote banking, call centers and other security-critical scenarios.
“When enrolling in voice authentication, you are asked to repeat a certain phrase in your own voice. The system then extracts a unique vocal signature (voiceprint) from this provided phrase and stores it on a server,” said Andre Kassis, a Computer Security and Privacy PhD candidate and the lead author of a study detailing the research.
“For future authentication attempts, you are asked to repeat a different phrase and the features extracted from it are compared to the voiceprint you have saved in the system to determine whether access should be granted.”
After the concept of voiceprints was introduced, malicious actors quickly realized they could use machine learning-enabled “deepfake” software to generate convincing copies of a victim’s voice using as little as five minutes of recorded audio.
In response, developers introduced “spoofing countermeasures” — checks that could examine a speech sample and determine whether it was created by a human or a machine.
The Waterloo researchers have developed a method that evades spoofing countermeasures and can fool most voice authentication systems within six attempts. They identified the markers in deepfake audio that betray it is computer-generated, and wrote a program that removes these markers, making it indistinguishable from authentic audio.
In a recent test against Amazon Connect’s voice authentication system, they achieved a 10 per cent success rate in one four-second attack, with this rate rising to over 40 per cent in less than thirty seconds. With some of the less sophisticated voice authentication systems they targeted, they achieved a 99 per cent success rate after six attempts.
Kassis contends that while voice authentication is obviously better than no additional security, the existing spoofing countermeasures are critically flawed.
“The only way to create a secure system is to think like an attacker. If you don’t, then you’re just waiting to be attacked,” Kassis said.
Kassis’ supervisor, computer science professor Urs Hengartner added, “By demonstrating the insecurity of voice authentication, we hope that companies relying on voice authentication as their only authentication factor will consider deploying additional or stronger authentication measures.” More

In a time of income inequality and ruthless politics, people with outsized power or an unrelenting willingness to browbeat others often seem to come out ahead.
New research from Dartmouth, however, shows that being uncooperative can help people on the weaker side of the power dynamic achieve a more equal outcome — and even inflict some loss on their abusive counterpart.
The findings provide a tool based in game theory — the field of mathematics focused on optimizing competitive strategies — that could be applied to help equalize the balance of power in labor negotiations or international relations and could even be used to integrate cooperation into interconnected artificial intelligence systems such as driverless cars.
Published in the latest issue of the journal PNAS Nexus, the study takes a fresh look at what are known in game theory as “zero-determinant strategies” developed by renowned scientists William Press, now at the University of Texas at Austin, and the late Freeman Dyson at the Institute for Advanced Study in Princeton, New Jersey.
Zero-determinant strategies dictate that “extortionists” control situations to their advantage by becoming less and less cooperative — though just cooperative enough to keep the other party engaged — and by never being the first to concede when there’s a stalemate. Theoretically, they will always outperform their opponent by demanding and receiving a larger share of what’s at stake.
But the Dartmouth paper uses mathematical models of interactions to uncover an “Achilles heel” to these seemingly uncrackable scenarios, said senior author Feng Fu, an associate professor of mathematics. Fu and first author Xingru Chen, who received her Ph.D. in mathematics from Dartmouth in 2021, discovered an “unbending strategy” in which resistance to being steamrolled not only causes an extortionist to ultimately lose more than their opponent but can result in a more equal outcome as the overbearing party compromises in a scramble to get the best payoff.

“Unbending players who choose not to be extorted can resist by refusing to fully cooperate. They also give up part of their own payoff, but the extortioner loses even more,” said Chen, who is now an assistant professor at the Beijing University of Posts and Telecommunications.
“Our work shows that when an extortioner is faced with an unbending player, their best response is to offer a fair split, thereby guaranteeing an equal payoff for both parties,” she said. “In other words, fairness and cooperation can be cultivated and enforced by unbending players.”
These scenarios frequently play out in the real world, Fu said. Labor relations provide a poignant model. A large corporation can strong-arm suppliers and producers such as farmworkers to accept lower prices for their effort by threatening to replace them and cut them off from a lucrative market. But a strike or protest can turn the balance of power back toward the workers’ favor and result in more fairness and cooperation, such as when a labor union wins some concessions from an employer.
While the power dynamic in these scenarios is never equal, Fu said, his and Chen’s work shows that unbending players can reap benefits by defecting from time to time and sabotaging what extortioners are truly after — the highest payoff for themselves.
“The practical insight from our work is for weaker parties to be unbending and resist being the first to compromise, thereby transforming the interaction into an ultimatum game in which extortioners are incentivized to be fairer and more cooperative to avoid ‘lose-lose’ situations,” Fu said.

“Consider the dynamics of power between dominant entities such as Donald Trump and the lack of unbending from the Republican Party, or, on the other hand, the military and political resistance to Russia’s invasion of Ukraine that has helped counteract incredible asymmetry,” he said. “These results can be applied to real-world situations, from social equity and fair pay to developing systems that promote cooperation among AI agents, such as autonomous driving.”
Chen and Fu’s paper expands the theoretical understanding of zero-determinant interactions while also outlining how the outsized power of extortioners can be checked, said mathematician Christian Hilbe, leader of the Dynamics of Social Behavior research group at the Max Planck Institute for Evolutionary Biology in Germany
“Among the technical contributions, they stress that even extortioners can be outperformed in some games. I don’t think that has been fully appreciated by the community before,” said Hilbe, who was not involved in the study but is familiar with it. “Among the conceptual insights, I like the idea of unbending strategies, behaviors that encourage an extortionate player to eventually settle at a fairer outcome.”
Behavioral research involving human participants has shown that extortioners may constitute a significant portion of our everyday interactions, said Hilbe, who published a 2016 paper in the journal PLOS ONE reporting just that. He also co-authored a 2014 study in Nature Communications that found people playing against a computerized opponent strongly resisted when the computer engaged in threatening conduct, even when it reduced their own payout.
“The empirical evidence to date suggests that people do engage in these extortionate behaviors, especially in asymmetric situations, and that the extorted party often tries to resist it, which is then costly to both parties,” Hilbe said. More

Making history with 42 digits: Scientists at Paderborn University and KU Leuven have unlocked a decades-old mystery of mathematics with the so-called ninth Dedekind number. Experts worldwide have been searching for the value since 1991. The Paderborn scientists arrived at the exact sequence of numbers with the help of the Noctua supercomputer located there. The results will be presented in September at the International Workshop on Boolean Functions and their Applications (BFA) in Norway.What started as a master’s thesis project by Lennart Van Hirtum, then a computer science student at KU Leuven and now a research associate at the University of Paderborn, has become a huge success. The scientists join an illustrious group with their work: Earlier numbers in the series were found by mathematician Richard Dedekind himself when he defined the problem in 1897, and later by greats of early computer science such as Randolph Church and Morgan Ward. “For 32 years, the calculation of D(9) was an open challenge, and it was questionable whether it would ever be possible to calculate this number at all,” Van Hirtum says.The previous number in the Dedekind sequence, the 8th Dedekind number, was found in 1991 using a Cray 2, the most powerful supercomputer at the time. “It therefore seemed conceivable to us that it should be possible by now to calculate the 9th number on a large supercomputer,” says Van Hirtum, describing the motivation for the ambitious project, which he initially implemented jointly with the supervisors of his master’s thesis at KU Leuven.Grains of sand, chess and supercomputersThe main subject of Dedekind numbers are so-called monotone Boolean functions. Van Hirtum explains, “Basically, you can think of a monotone Boolean function in two, three, and infinite dimensions as a game with an n-dimensional cube. You balance the cube on one corner and then color each of the remaining corners either white or red. There is only one rule: you must never place a white corner above a red one. This creates a kind of vertical red-white intersection. The object of the game is to count how many different cuts there are. Their number is what is defined as the Dedekind number. Even if it doesn’t seem like it, the numbers quickly become gigantic in the process: the 8th Dedekind number already has 23 digits.”Comparably large – but incomparably easier to calculate – numbers are known from a legend concerning the invention of the game of chess. “According to this legend, the inventor of the chess game asked the king for only a few grains of rice on each square of the chess board as a reward: one grain on the first square, two grains on the second, four on the third, and twice as many on each of the following squares. The king quickly realized that this request was impossible to fulfill, because so much rice does not exist in the whole world. The number of grains of rice on the complete board would have 20 digits – an unimaginable amount, but still less than D(8). When you realize these orders of magnitude, it is obvious that both an efficient computational method and a very fast computer would be needed to find D(9),” Van Hirtum said.Milestone: Years become months To calculate D(9), the scientists used a technique developed by master’s thesis advisor Patrick De Causmaecker known as the P-coefficient formula. It provides a way to calculate Dedekind numbers not by counting, but by a very large sum. This allows D(8) to be decoded in just eight minutes on a normal laptop. But, “What takes eight minutes for D(8) becomes hundreds of thousands of years for D(9). Even if you used a large supercomputer exclusively for this task, it would still take many years to complete the calculation,” Van Hirtum points out. The main problem is that the number of terms in this formula grows incredibly fast. “In our case, by exploiting symmetries in the formula, we were able to reduce the number of terms to ‘only’ 5.5*10^18 – an enormous amount. By comparison, the number of grains of sand on Earth is about 7.5*10^18, which is nothing to sneeze at, but for a modern supercomputer, 5.5*10^18 operations are quite manageable,” the computer scientist said. The problem: The calculation of these terms on normal processors is slow and also a use of GPUs as currently the fastest hardware accelerator technology for many AI applications is not efficient for this algorithm.The solution: application-specific hardware using highly specialized and parallel arithmetic units – so-called FPGAs (field programmable gate arrays). Van Hirtum developed an initial prototype for the hardware accelerator and began looking for a supercomputer that had the necessary FPGA cards. In the process, he became aware of the Noctua 2 computer at the “Paderborn Center for Parallel Computing (PC2)” at the University of Paderborn, which has one of the world’s most powerful FPGA systems.Prof. Dr. Christian Plessl, head of PC2, explains: “When Lennart Van Hirtum and Patrick De Causmaeker contacted us, it was immediately clear to us that we wanted to support this moonshot project. Solving hard combinatorial problems with FPGAs is a promising field of application and Noctua 2 is one of the few supercomputers worldwide with which the experiment is feasible at all. The extreme reliability and stability requirements also pose a challenge and test for our infrastructure. The FPGA expert consulting team worked closely with Lennart to adapt and optimize the application for our environment.”After several years of development, the program ran on the supercomputer for about five months. And then the time had come: on March 8, the scientists found the 9th Dedekind number: 286386577668298411128469151667598498812366.Today, three years after the start of the Dedekind project, Van Hirtum is working as a fellow of the NHR Graduate School at the Paderborn Center for Parallel Computing to develop the next generation of hardware tools in his PhD. The NHR (National High Performance Computing) Graduate School is the joint graduate school of the NHR centers. He will report on his extraordinary success together with Patrick De Causmaecker on June 27 at 2 p.m. in Lecture Hall O2 of the University of Paderborn. The interested public is cordially invited. More