New physics research reveals how math transforms the testing of partially entangled quantum systems, improving device accuracy.
Category: mathematics – Page 11
Mathematicians uncover the hidden patterns behind a $3.5 billion cryptocurrency collapse
In a new study published in ACM Transactions on the Web, researchers from Queen Mary University of London have unveiled the intricate mechanisms behind one of the most dramatic collapses in the cryptocurrency world: the downfall of the TerraUSD stablecoin and its associated currency, LUNA. Using advanced mathematical techniques and cutting-edge software, the team has identified suspicious trading patterns that suggest a coordinated attack on the ecosystem, leading to a catastrophic loss of $3.5 billion in value virtually overnight.
The study, led by Dr. Richard Clegg and his team, employs temporal multilayer graph analysis—a sophisticated method for examining complex, interconnected systems over time. This approach allowed the researchers to map the relationships between different cryptocurrencies traded on the Ethereum blockchain, revealing how the TerraUSD stablecoin was destabilized by a series of deliberate, large-scale trades.
Stablecoins like TerraUSD are designed to maintain a steady value, typically pegged to a fiat currency like the US dollar. However, in May 2022, TerraUSD and its sister currency, LUNA, experienced a catastrophic collapse. Dr. Clegg’s research sheds light on how this happened, uncovering evidence of a coordinated attack by traders who were betting against the system, a practice known as “shorting.”
Hidden Geometries: The Search for Extra Dimensions and Their Technological Implications
Whether extra dimensions prove to be physical realities or useful mathematical constructs, they have already transformed our understanding of the universe. They have forced us to reconsider fundamental assumptions about space, time, and the nature of physical law. And they remind us that reality may be far richer and more complex than our everyday experience suggests — that beyond the familiar dimensions of length, width, height, and time, there may exist entire realms waiting to be discovered and, perhaps one day, explored.
The theoretical physicist John Wheeler once remarked that “we live on an island of knowledge surrounded by an ocean of ignorance.” Our exploration of extra dimensions extends the shoreline of that island, pushing into uncharted waters with the tools of mathematics, experiment, and imagination. Though we may never set foot in the fifth dimension or beyond, the very act of reaching toward these hidden aspects of reality expands our perspective and deepens our understanding of the cosmos we call home.
As we continue this grand scientific adventure, we carry forward the legacy of those who first dared to imagine worlds beyond our immediate perception — from the mathematicians who developed the language of higher-dimensional geometry to the physicists who incorporated these concepts into our most fundamental theories. Their vision, coupled with rigorous analysis and experimental testing, illuminates a path toward an ever more complete understanding of the universe in all its dimensions.
The Reconstructability of Networks
Network models provide a flexible way of representing objects and their multifaceted relationships. Deriving a network entails mapping hidden structures in inevitably noisy data—a critical task known as reconstruction. Now Gang Yan and Jia-Jie Qin of Tongji University in China have provided a mathematical proof showing what makes some networks easier to reconstruct than others [1].
Complex systems in biology, physics, and social sciences tend to involve a vast number of interacting entities. In a network model, these entities are represented by nodes, linked by connections weighted to describe the strength of each interaction. Yan and Qin took an empirical dataset and used a statistical inference method to calculate the likelihood that any pair of nodes is directly linked. Then, based on the true positive and false positive rates of these inferred connections, they analyzed the fidelity of the reconstructed networks. They found that the most faithful reconstructions are obtained with systems for which the number of connections per node varies most widely across the network. Yan and Qin saw the same tendency when they tested their model on synthetic and real networks, including metabolic networks, plant-pollinator webs, and power grids.
With the rapid increase in available data across research areas, network reconstruction has become an important tool for studying complex systems. Yan and Qin say their new result both solves the problem of what complex systems can be easily mapped into a network and provides a solid foundation for developing methods of doing so.
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Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. One goes into the first room, and it’s dark, completely dark. One stumbles around bumping into the furniture, and gradually, you learn where each piece of furniture is, and finally, after six months or so, you find the light switch. You turn it on, and suddenly, it’s all illuminated. You can see exactly where you were.
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New study challenges the story of humanity’s shift from prehistoric hunting to farming
A new study published in Proceedings of the National Academy of Sciences has turned traditional thinking on its head by highlighting the role of human interactions during the shift from hunting and gathering to farming—one of the biggest changes in human history—rather than earlier ideas that focused on environmental factors.
The transition from a hunter-gatherer foraging lifestyle, which humanity had followed for hundreds of thousands of years, to a settled farming one about 12,000 years ago has been widely discussed in popular books like “Sapiens: A Brief History of Humankind” by Yuval Noah Harari.
Researchers from the University of Bath, the Max Planck Institute for Evolutionary Anthropology in Germany, the University of Cambridge, UCL, and others have developed a new mathematical model that challenges the traditional view that this major transition was driven by external factors, such as climate warming, increased rainfall, or the development of fertile river valleys.
AI in the Classroom Can Make Higher Education Much More Accessible
Summary: ChatGPT4 has demonstrated superiority in various student exams, revealing its potential to support academic learning and improve educational outcomes, particularly in test preparation. With its accessibility and affordability compared to traditional tutoring services, AI tutoring can help address the increasing demand for academic support, especially as universities begin to reinstate standardized testing requirements.
In 2023, OpenAI shook the foundation of the education system by releasing ChatGPT4. The previous model of ChatGPT had already disrupted classrooms K–12 and beyond by offering a free academic tool capable of writing essays and answering exam questions. Teachers struggled with the idea that widely accessible artificial intelligence (AI) technology could meet the demands of most traditional classroom work and academic skills. GPT3.5 was far from perfect, though, and lacked creativity, nuance, and reliability. However, reports showed that GPT4 could score better than 90 percent of participants on the bar exam, LSAT, SAT reading and writing and math, and several Advanced Placement (AP) exams. This showed a significant improvement from GPT3.5, which struggled to score as well as 50 percent of participants.
This marked a major shift in the role of AI, from it being an easy way out of busy work to a tool that could improve your chances of getting into college. The US Department of Education published a report noting several areas where AI could support teacher instruction and student learning. Among the top examples was intelligent tutoring systems. Early models of these systems showed that an AI tutor could not only recognize when a student was right or wrong in a mathematical problem but also identify the steps a student took and guide them through an explanation of the process.
