Phys.org Mathmatics

• How long does it take to get last liquid drops from kitchen containers? These physicists know the answer

  At some point, most people have found themselves holding a tilted carton of milk or bottle of cooking oil, patiently waiting for the last drops to drip out. Now, physicists at Brown University have done the math to show just how long you might have to wait.

• Putting sports stats to the test: Unpredictable play helps pick a winner in soccer

  A comprehensive game plan and strategic tactics are critical to winning soccer, but how much does a team's unpredictability in moving the soccer ball around the pitch matter? In a new article published in PLOS One, an international team of researchers analyzed event data from top-tier association soccer competitions to provide insights into match analysis, player tactics and game strategy.

• Probability underlies much of the modern world—an engineering professor explains how it actually works

  Probability underpins AI, cryptography and statistics. However, as the philosopher Bertrand Russell said, "Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means."

• How choices made by crowds in a train station are guided by strangers

  In crowds, most people are strangers to you, and everyone else for that matter. However, until now, the effect of stranger-to-stranger interactions on the choices people make in crowds has not been properly examined. Ziqi Wang and Federico Toschi from the TU/e Department of Applied Physics and Science Education, along with Alessandro Gabbana at the University of Ferrara in Italy, explored how strangers influence people's choices in crowds at Eindhoven Centraal railway station. The research is published in the journal Proceedings of the National Academy of Sciences.

• Why some tunes stick: Mathematical symmetry helps explain catchy melodies

  Why do some melodies feel instantly right, balanced, memorable and satisfying, even if you have never heard them before? New research from the University of Waterloo suggests that more than creativity is at play.

• From life events to travel trends, DEMOS tool brings demographic realism to transportation modeling

  Many personal transportation-related decisions—such as vehicle purchases—are influenced by life events, like the birth of a child or a change in employment. Modeling tools that reflect how life trajectories evolve over time enable researchers and planners to more effectively assess how people might adopt new transportation technologies.

• From power grids to epidemics: Study shows how small patterns trigger systemic failures

  Why do some systems collapse suddenly after what seems like a minor disturbance? A single transmission line failure can cascade into widespread blackouts. A delayed shipment can ripple through a global supply chain, emptying store shelves far from the original disruption. A rumor spreading in a small online network can spark nationwide panic. In nature, a slight environmental shift can throw an ecosystem into chaos, and a local disease outbreak can quickly escalate into an epidemic.

• AI system TongGeometry generates and solves olympiad-level geometry problems

  The International Mathematical Olympiad (IMO) is a prestigious competition featuring talented high school students from around the world, in which competitors solve complicated mathematical problems. Geometry problems from these kinds of competitions—in particular, the formal logic and spatial reasoning involved—has been noted as a critical benchmark in artificial intelligence (AI) research.

• From cells to companies: Study shows how diversity scales within complex systems

  A mystery novel, a history book, and a fantasy epic may have little in common in plot or style. But count the words inside them and a strange regularity appears: many new words show up early, then fewer and fewer as the author reuses what has already been introduced. That pattern, known as Heaps' law, turns out not to belong to books alone. A new study published in the Proceedings of the National Academy of Sciences finds that the same rule also describes how many complex systems grow, from living cells and corporations to universities and government agencies—and could even be used to predict how they will change in the future.

• Passing got faster and more accurate in top soccer leagues, study finds

  The amount and accuracy of passing in the game of soccer—called football across much of the world—has climbed in recent years, according to new research. The average passing volume, pass accuracy, and the percentage of passes made rose in gameplay over the last five years, with the biggest changes occurring in women's competitions, according to an article posted to the arXiv preprint server from the Network Science Sports Institute, or NetSi Sport, a new research group out of Northeastern University's Network Science Institute. Gameplay has become faster and more intense, suggesting there is greater defensive pressure.

• When you do the math, humans still rule

  Artificial intelligence has attained an impressive series of feats—solving problems from the International Math Olympiad, conducting encyclopedic surveys of academic literature, and even finding solutions to some longstanding research questions. Yet these systems largely remain unable to match top experts in the conceptual frontiers of research math. Have reports of AI replacing mathematicians been greatly exaggerated?

• Exploring why some children struggle to learn math

  Hyesang Chang and colleagues, from Stanford University, explored why some children struggle to learn math compared to their peers in a new JNeurosci paper. Children selected which numbers were bigger than others across different trials, with quantities represented as numerical symbols or as clusters of dots. The researchers created a model based on how much performance varied over time. The model suggested that children with difficulties in learning math struggled to update their thinking approach as they continued to get different types of trials wrong.

• Why elite chess ratings get stuck: A new model treats draws as data

  Here's a statistical challenge worthy of a grandmaster: How do you create an accurate ranking system when the best players usually don't win? This is the conundrum of elite chess. The stronger the players, the greater the odds of the match ending in a draw.

• Leading AI models struggle to solve original math problems

  Mathematics, like many other scientific endeavors, is increasingly using artificial intelligence. Of course, math is the backbone of AI, but mathematicians are also turning to these tools for tasks like literature searches and checking manuscripts for errors. But how well can AI perform when it comes to solving genuine, high-level research problems?

• A 'crazy' dice proof leads to a new understanding of a fundamental law of physics

  Right now, molecules in the air are moving around you in chaotic and unpredictable ways. To make sense of such systems, physicists use a law known as the Boltzmann distribution, which, rather than describe exactly where each particle is, describes the chance of finding the system in any of its possible states. This allows them to make predictions about the whole system even though the individual particle motions are random. It's like rolling a single die: Any one roll is unpredictable, but if you keep rolling it again and again, a pattern of probabilities will emerge.

• A digital game improves the mathematical performance of children with dyscalculia

  Dyscalculia, characterized by deficits in number sense and calculation skills, affects approximately 5%–7% of the population and often persists into adulthood. A team from the University of Barcelona and the University of Vic—Central University of Catalonia (UVic-UCC) has developed and validated a digital game to address mathematical difficulties in children with this disorder in the early and middle stages of primary education.

• AI systems could identify math anxiety from student inputs and change feedback

  Math anxiety is a significant challenge for students worldwide. While personalized support is widely recognized as the most effective way to address it, many teachers struggle to deliver this level of support at scale within busy classrooms. New research from Adelaide University shows how artificial intelligence (AI) could help address challenges such as math anxiety by using a student's inputs and identifying signs of anxiety or disengagement during learning.

• Beyond the eye of the beholder: Mathematically defining attributes essential to color perception

  Research on the perception of color differences is helping resolve a century-old understanding of color developed by Erwin Schrödinger. Los Alamos scientist Roxana Bujack led a team that used geometry to mathematically define the perception of color as it relates to hue, saturation and lightness.

• Q&A: Even small amounts of online math practice can improve skills

  An analysis of data from 200,000 students using a computer-assisted math program supports an optimistic view of skill-focused, mastery-based learning, even with limited use.

• Knock, knock... mapping comedic timing with a computational framework

  Researchers propose a computational method to reveal the hidden timing structure of live performance. Vanessa C. Pope and colleagues present a framework, called Topology Analysis of Matching Sequences (TAMS), that algorithmically detects repeated material across performances and maps its timing to visualize performance dynamics. The work is published in PNAS Nexus.

• Living together with differences: Mathematical model shows how to reduce social friction without forcing consensus

  Opinion polarization is often considered as the primary driver of social friction, leading to exhaustive efforts to force a consensus. However, new research suggests a more pragmatic goal: reducing the friction of disagreement without necessarily eliminating the diversity of opinion.

• How gender bias influences math education

  Young children are more inclined to believe incorrect math information from men than accurate information from women, according to a Rutgers University–New Brunswick study published in the journal Developmental Science.

• 'Nu' citation index may bridge gap between productivity and impact metrics

  Researchers propose a new citation index that balances productivity and impact in academic publishing. The h-index of citations was introduced in 2005 by physicist Jorge E. Hirsch. This index is defined simply as the maximum number h of an author's published papers with at least h citations each. For example, h = 3 means that there are three papers with 3 or more citations, but if a fourth paper exists, it has fewer than four citations.

• Nature-inspired computers are shockingly good at math

  Neuromorphic computers, inspired by the architecture of the human brain, are proving surprisingly adept at solving complex mathematical problems that underpin scientific and engineering challenges.

• Chess960's random setups still favor white, new study reveals

  Chess is a relatively simple game to learn but a very difficult one to master. Because the starting positions of the pieces are fixed, top players have relied on memorizing the "best" opening moves, which can sometimes result in boring, predictable games. To encourage more creative play and move away from pure memory, former world champion Bobby Fischer proposed Chess960 in the 1990s.