Phys.org Mathmatics

• Art analysis: 2D multifractal tools examine Jackson Pollock's expressionism

  The temperature changes hour to hour and day to day; exchange rates behave no differently. Wherever studies of the variability of similar one-dimensional time series are concerned, analyses based on multifractals have managed to gain recognition. Now, these tools have been developed and successfully applied to two-dimensional cases, including the study of abstract paintings by Jackson Pollock.

• Mathematical technique 'opens the black box' of AI decision-making

  Western researchers have developed a novel technique using math to understand exactly how neural networks make decisions—a widely recognized but poorly understood process in the field of machine learning.

• English children lag behind in geometry, but parents can help them learn through play

  Geometry is an important branch of mathematics, which we use to understand the properties of 2D and 3D space such as distance, shape, size and position. We use geometry every day: cutting paper to wrap a present, calculating the area of a room to tile a floor, and interpreting pie charts and bar graphs at work. Even noticing when a picture on the wall is askew draws on our geometrical understanding.

• Mathematicians develop new method to forecast natural phenomena and detect early cancer development

  Partial Differential Equations (PDEs) are central to both pure and applied mathematics. Any quantity which changes in space and time will satisfy certain partial differential equations because the laws of nature, and the laws of physics specifically, relate a quantity to its rate of change in space and time.

• Historian explains how economics research stumbled under Soviet regime, while mathematics thrived

  Political and ideological barriers can shape the progress of academic disciplines, warns Ivan Boldyrev. In a paper appearing in the Journal of Economic Literature , the historian of economics at Radboud University explores the complex history of Soviet science and warns that a new Cold War might once again hinder academic progress.

• How does a hula hoop master gravity? Mathematicians prove that body shape matters

  Hula hooping is so commonplace that we may overlook some interesting questions it raises: "What keeps a hula hoop up against gravity?" and "Are some body types better for hula hooping than others?" A team of mathematicians explored and answered these questions with findings that also point to new ways to better harness energy and improve robotic positioners.

• Researcher calculates Santa's speed on Christmas Eve—and this is what it would do to Rudolph's nose

  With billions of children around the world anxiously waiting for their presents, Father Christmas (or Santa) and his reindeer must be traveling at breakneck speeds to deliver them all in one night.

• Algebraic geometry offers fresh solution to data center energy inefficiency

  The manic pace of sharing, storing, securing, and serving data has a manic price—power consumption. To counter this, Virginia Tech mathematicians are leveraging algebraic geometry to target the inefficiencies of data centers.

• How prepared are we for another pandemic? Study provides mathematical insights into airborne viral transmission

  Half a decade on from the start of the COVID-19 pandemic, a study by the University of Surrey highlights the significant impact of combined public health measures in reducing airborne viral transmission. High-quality face masks were shown to reduce transmission risk by ninefold, while doubling indoor air ventilation cut the risk by nearly a third, providing valuable insights to support future prevention strategies for respiratory diseases. The research is published in the journal Physical Review E.

• String figures shed light on cultural connections and the roots of mathematical reasoning

  A collaborative study between the University of Helsinki, Aarhus University, the National Museum of Denmark and Seattle University examined the cognitive, cultural and historical significance of traditional string figures. The study explored whether certain string figures evolved independently in different parts of the world or share a common ancestry.

• Can deep learning techniques predict sudden state transitions in nonlinear dynamical systems?

  Nonlinear dynamical systems are systems that can undergo sudden shifts not due to changes in their state or stability, but in response to the rate at which external conditions or parameters change. These sudden shifts, known as noise-induced and rate-induced tipping, can make predicting how the systems will shift over time more challenging.

• How much faster is a knight than a king? A mathematical study reveals the exact ratio

  We know a knight can move across the chessboard faster than the king, but exactly how much faster? Christian Táfula Santos, a doctoral student in UdeM's Department of Mathematics, has done the math and his proof has been published on the pre-print server arXiv.

• Mathematician solves the moving sofa problem

  A mathematician at Yonsei University, in Korea, claims to have solved the moving sofa problem. Jineon Baek has posted a 100+-page proof of the problem on the arXiv preprint server.

• 'I was scared': Many student teachers had bad math experiences at school. Here's how they can do better

  What do you remember about math at school? Did you whizz through the problems and enjoy getting the answers right? Or did you often feel lost and worried you weren't keeping up? Perhaps you felt math wasn't for you and you stopped doing it altogether.

• Mathematicians make leap in modeling human impact on climate

  A breakthrough in the theory of climate change science has given scientists the most robust way yet to link observed climate change to both human-made and natural causes and to spot early warning signals for potential climate disasters.

• Physics-based models combined with big data could lead to systematically better hypotheses

  Finding a reasonable hypothesis can pose a challenge when there are thousands of possibilities. This is why Dr. Joseph Sang-II Kwon is trying to make hypotheses in a generalizable and systematic manner.

• Hybrid model links micro and macro scales in complex systems

  In fields ranging from immunology and ecology to economics and thermodynamics, multi-scale complex systems are ubiquitous. They are also notoriously difficult to model. Conventional approaches take either a bottom-up or top-down approach. But in disturbed systems, such as a post-fire forest ecosystem or a society in a pandemic, these unidirectional models can't capture the interactions between the small-scale behaviors and the system-level properties. SFI External Professor John Harte (UC Berkeley) and his collaborators have worked to resolve this challenge by building a hybrid method that links bottom-up behaviors and top-down causation in a single theory.

• Love thy neighbor: Researchers reveal network structures that enhance cooperation throughout a system

  Helping out your neighbor or minding your own business? A challenging choice with different benefits for each decision. Game theory provides guidance in making such choices—from a theoretical perspective.

• Why are boys outperforming girls in math?

  A major international test has revealed a concerning gender gap in math among Australian school students.

• Can we avert the looming food crisis of climate change? Mathematical model reveals critical threshold

  Human activities are causing atmospheric carbon dioxide (CO2) levels to rise, which increases the global average surface temperature—and poses a threat to crop growth. Escalating concerns about climate change's impact on global food security inspired researchers from Banaras Hindu University in India to create a way to explore how these factors influence crop yields.

• Mathematicians develop AI to forecast market interest rates

  Researchers from the Ateneo de Manila University have developed artificial intelligence (AI) deep learning tools that can help predict money market interest rates, invaluable for decision-makers in business and government.

• A new puzzle piece for string theory research: Study proves 4-graviton scattering conjecture

  String theory aims to explain all fundamental forces and particles in the universe—essentially, how the world operates on the smallest scales. Though it has not yet been experimentally verified, work in string theory has already led to significant advancements in mathematics and theoretical physics.

• Mathematical approach can predict crystal structure in hours instead of months

  Researchers at New York University have devised a mathematical approach to predict the structures of crystals—a critical step in developing many medicines and electronic devices—in a matter of hours using only a laptop, a process that previously took a supercomputer weeks or months. Their novel framework is published in the journal Nature Communications.

• A 41-million-digit prime number is the biggest ever found—but mathematicians' search for perfection will continue

  Imagine a number made up of a vast string of ones: 1111111…111. Specifically, 136,279,841 ones in a row. If we stacked up that many sheets of paper, the resulting tower would stretch into the stratosphere.

• Flexible statistical method powers research on health, climate, financial data

  Machine learning and artificial intelligence wouldn't be possible without the statistical models that underpin their analytic capabilities. A Cornell statistician and his colleague have developed a revolutionary new method to analyze complex datasets that's more flexible, accurate and easy to use.