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Abstract algebra and algebraic geometry to connect quantum physics with number theory Several fields of mathematics have developed in total isolation, using their own 'undecipherable' coded languages. In a new study published in PNAS , Tamás Hausel, professor of mathematics at the Institute of Science and Technology Austria (ISTA), presents "big algebras," a two-way mathematical 'dictionary' between symmetry, algebra, and geometry, that could strengthen the connection between the distant worlds of quantum physics and number theory.

Publication of the Physics Laboratory in the Physical Review Letters on July 31, 2024. Communication by CNRS Physics on September 2, 2024. Experiments on a classical microscopic system show that, while the second principle of thermodynamics is still valid on average, it can be circumvented experimentally in 95% of cases! A study conducted at the Physics Laboratory of ENS de Lyon, published in Physical Review Letters .

The way we memorise information - a mathematical problem statement, for example - reveals the way we process it. A team from the University of Geneva , in collaboration with CY Cergy Paris University (CYU) and Bourgogne University (uB), has shown how different solving methods can alter the way information is memorised and even create false memories.

In new research, TU/e's Mireille Boutin has obtained major results that help improve GPS technologies using unconventional mathematical techniques. The summer holidays are ending, which for many concludes with a long drive home and reliance on GPS devices to get safely home. But every now and then, GPS devices can suggest strange directions or get briefly confused about your location.

The first comprehensive model of rotor aerodynamics could improve the way turbine blades and wind farms are designed and how wind turbines are controlled. The blades of propellers and wind turbines are designed based on aerodynamics principles that were first described mathematically more than a century ago.

Researchers have published a programmable framework that overcomes a key computational bottleneck of optics-based artificial intelligence systems. In a series of image classification experiments, they used scattered light from a low-power laser to perform accurate, scalable computations using a fraction of the energy of electronics.

Researcher at the Cluster of Excellence Mathematics finds an approach that can be used flexibly Whether it's physical phenomena, share prices or climate models - many dynamic processes in our world can be described mathematically with the aid of partial differential equations. Thanks to stochastics - an area of mathematics which deals with probabilities - this is even possible when randomness plays a role in these processes.

Through a novel approach, Yale researchers translate data from monkeys to better understand how paranoia arises in the human brain. The capacity to adjust beliefs about one's actions and their consequences in a constantly changing environment is a defining characteristic of advanced cognition. Disruptions to this ability, however, can negatively affect cognition and behavior, leading to such states of mind as paranoia, or the belief that others intend to harm us.

Boys are good at math, girls not so much? A study from the University of Zurich has analyzed the social mechanisms that contribute to the gender gap in math confidence. While peer comparisons seem to play a crucial role for boys, girls' subjective evaluations are more likely to be based on objective performance.

Researchers have developed a platform for the interactive evaluation of AI-powered chatbots such as ChatGPT. Anyone using an LLM, for any application, should always pay attention to the output and verify it themselves Albert Jiang A team of computer scientists, engineers, mathematicians and cognitive scientists, led by the University of Cambridge, developed an open-source evaluation platform called CheckMate, which allows human users to interact with and evaluate the performance of large language models (LLMs).

A simple concept of decay and fission of "magnetic quivers" helps to clarify complex quantum physics and mathematical structures.

Whether performed by a human or a computer, matrix multiplication is a tedious task. Researchers are battling to reduce the time and number of steps required to solve this type of operation. Excel spreadsheets, climate modeling, simulation of aircraft wing structure, neural network calculations, image processing.

A new technique that can automatically classify phases of physical systems could help scientists investigate novel materials. When water freezes, it transitions from a liquid phase to a solid phase, resulting in a drastic change in properties like density and volume. Phase transitions in water are so common most of us probably don't even think about them, but phase transitions in novel materials or complex physical systems are an important area of study.

Researchers at EPFL use neural networks to study proprioception, the sense the brain uses to "know" the body's movement and position. How does your brain know the position and movement of your different body parts? The sense is known as proprioception, and it is something like a "sixth sense", allowing us to move freely without constantly watching our limbs.

Research by UC3M and Johns Hopkins University Scientists from Universidad Carlos III de Madrid (UC3M) and Johns Hopkins University (JHU), in the USA, have analyzed the growth of breast tumors from a biomechanical perspective and have created a computational model that simulates the invasion process of cancer cells, depending on the characteristics of the surrounding tissue and cell junctions, among other parameters.

Researchers from TU/e and the University of Chicago discovered how to manipulate turbulent flows to create regular patterns like those seen in the tabby coat pattern of a cat. The new research has been published in Nature. Controlling the chaos of a turbulent flow to make regular patterns sounds like a contradiction in every sense of the word.

Scientists show that our mental representations of mathematical problems influence our strategies for solving them. Solving arithmetic problems, even simple subtractions, involves mental representations whose influence remains to be clarified. Visualizing these representations would enable us to better understand our reasoning and adapt our teaching methods.

Faster and more accurate than some alternatives, this approach could be useful for robots that interact with humans or work in tight spaces. Before a robot can grab dishes off a shelf to set the table, it must ensure its gripper and arm won't crash into anything and potentially shatter the fine china.

Scientists at ISTA present a new mathematic model for cooperation Human coexistence depends on cooperation. Individuals have different motivations and reasons to collaborate, resulting in social dilemmas, such as the well-known prisoner's dilemma. Scientists from the Chatterjee group at the Institute of Science and Technology Austria (ISTA) now present a new mathematical principle that helps to understand the cooperation of individuals with different characteristics.

An easy-to-use technique could assist everyone from economists to sports analysts. Pollsters trying to predict presidential election results and physicists searching for distant exoplanets have at least one thing in common: They often use a tried-and-true scientific technique called Bayesian inference.