Toggle light / dark theme

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.

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.


Add a note Draw a rectangle onto the image above (press the left mouse button, then drag and release). This file has annotations. Move the mouse pointer over the image to see them. To edit the notes, visit page X. Why do you want to remove this note?

Save Help about image annotations This file has annotations To modify annotations, your browser needs to have the XMLHttpRequest object. Your browser does not have this object or does not allow it to be used (in Internet Explorer, it may be in a switched off ActiveX component), and thus you cannot modify annotations. We’re sorry for the inconvenience.

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 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.

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.

The DeepSeek-V3-0324, named after its predecessor and the launch date, has “enhanced reasoning capabilities, optimised front-end web development and upgraded Chinese writing proficiency”, according to a notice on the company’s website.

The new version and DeepSeek V3 are both foundation models trained on vast data sets that can be applied in different use cases, including that of a chatbot. DeepSeek R1, the reasoning model, is based on DeepSeek V3.

The updated foundation model has made improvements in several benchmarks, especially the American Invitational Mathematics Examination (AIME), where it scored 59.4 compared with 39.6 for its predecessor, while achieving an increase of 10 points on LiveCodeBench to achieve 49.2, DeepSeek data showed.

Pedestrian crossings generally showcase the best in pedestrian behavior, with people naturally forming orderly lanes as they cross the road, smoothly passing those coming from the opposite direction without any bumps or scrapes. Sometimes, however, the flow gets chaotic, with individuals weaving through the crowd on their own haphazard paths to the other side.

Now, an international team of mathematicians, co-led by Professor Tim Rogers at the University of Bath in the UK and Dr. Karol Bacik at MIT in the US has made an important breakthrough in their understanding of what causes human flows to disintegrate into tangles. This discovery has the potential to help planners design road crossings and other pedestrian spaces that minimize chaos and enhance safety and efficiency.

In a paper appearing in the journal Proceedings of the National Academy of Sciences, the team pinned down the precise point at which crowds of pedestrians crossing a road collapse from order to disorder.

In the ebb and flow of crowded crosswalks, a surprising pattern emerges: people can naturally form neat lanes of movement. But what flips the switch from graceful organization to chaotic weaving?

An international team of researchers has pinpointed a specific tipping point: when pedestrians deviate more than 13 degrees from their path, order collapses. Backed by math, experiments, and real-world testing, this discovery could revolutionize how cities manage foot traffic.

From flow to frenzy: what disrupts pedestrian order?