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New AI math tool could sharpen image editing, drug discovery and simulations

Clarkson University researchers have developed a new mathematical tool that could make artificial intelligence systems more accurate, controllable and useful across applications ranging from image editing to drug discovery.

Clarkson University postdoctoral researcher Zander Blasingame and Chen Liu, professor of electrical and computer engineering, created a new family of numerical solvers called Rex that improves how generative AI models move between random noise and meaningful data. Their work, “Rex: A Family of Reversible Exponential (Stochastic) Runge-Kutta Solvers,” will be presented this summer at the International Conference on Machine Learning (ICML 2026), and an earlier version of the paper is available on the arXiv preprint server.

Diffusion and flow-matching models are the foundation of many modern generative AI systems, including image generators, molecular design tools and scientific simulators. They work by gradually transforming random noise into useful outputs. While that process is effective for creating new content, many important applications require running it in reverse. Existing methods often introduce errors that make it difficult to accurately recover the original information.

Corrected microbial family tree offers statistically sound model for how earliest life forms evolved

In this era of Big Data, the prevailing wisdom is that more information leads to better answers. However, a new Canadian study shows that in the hunt for life’s ancient ancestors, more data can actually lead to less truth. Published in the Proceedings of the National Academy of Sciences, the research by UdeM associate professor of computer science Miklós Csűrös reveals that standard methods for reconstructing the genomes of ancient microbes are being overwhelmed by an explosion of information.

This paradox causes current models to “hallucinate” evolutionary events—specifically, an implausibly high number of horizontal gene transfers—that are actually just statistical ghosts, the study shows.

In it, Csűrös identifies a crisis point in evolutionary biology: As researchers try to reconcile thousands of gene sequences across the entire tree of life, the actual evolutionary signal begins to vanish, replaced by mathematical noise.

How do flocking birds and schools of fish move? New research offers crystal-clear answer

Flocking birds and schools of fish are a familiar sight. While previous research has uncovered the broad dynamics driving these movements, their underlying intricacies remain a mystery. Now a study by a team of New York University mathematicians offers new insights into these phenomena. It reveals that flocks and schools behave in ways similar to a soft crystalline material, with individual birds and fish serving as “atoms” that are evenly spaced in a lattice-like formation.

The findings, reported in the journal Physical Review Fluids, offer detailed insights into the hydrodynamic and aerodynamic interactions crucial in aerospace and automotive engineering, robotics and energy harvesting.

“Our findings offer a new way to understand how animal collectives coordinate movement and respond to their environment,” says Christiana Mavroyiakoumou, a researcher at NYU’s Courant Institute School of Mathematics, Computing, and Data Science at the time of the study and now a fellow at Oxford University’s Mathematical Institute. “More specifically, lines of birds or fish behave like an elastic material with regularly spaced individuals held together by flexible, or spring-like, bonds—akin to soft crystalline substances in which atoms are arranged in an orderly, repeating pattern.”

How Divergence and Curl Were Discovered

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This video is about how Divergence and Curl, along with the theory of Vector Analysis was discovered.

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Image Credits:
https://commons.wikimedia.org/wiki/Fi…, https://creativecommons.org/licenses/.… Approaching a Black Hole: NASA’s Scientific Visualization Studio — Caltech-IPAC/Robert Hurt, Caltech-IPAC/Keith Miller, NASA/JPL/Chelsea Gohd, Global Science and Technology, Inc./Ella Kaplan, NASA/GSFC/Mark SubbaRao Many more images that are public domain from wikimedia commons _____ Sources: Vector, A Surprising Story of Space, Time, and Mathematical Transformation by Robyn Arianrhod A History of Vector Analysis by Michael J. Crose Maxwell’s Treatise on Electricity and Magnetism + A Dynamical Theory of the Electromagnetic Field Great videos by Kathy Loves Physics: • Quaternions are Amazing and so is William…, • How Maxwell’s Equations (and Quaternions)… _____ Corrections: 15:12 — on screen it should read “born in Scotland 1831″ instead of 1931 _____ Music: Epidemic Sound Animations created using Manim: https://www.manim.community/ Illustrations and Thumbnails: Christine Kosakowski This video was sponsored by Surfshark.
https://commons.wikimedia.org/wiki/Fi…, https://creativecommons.org/licenses/.
Approaching a Black Hole: NASA’s Scientific Visualization Studio — Caltech-IPAC/Robert Hurt, Caltech-IPAC/Keith Miller, NASA/JPL/Chelsea Gohd, Global Science and Technology, Inc./Ella Kaplan, NASA/GSFC/Mark SubbaRao.

Many more images that are public domain from wikimedia commons.

Penrose vs EWOG: Consciousness and Quantum Collapse

Consciousness beyond penrose quantum microtubules?utm_source=share&utm_medium=member_android&rcm=ACoAADcXNX8BNm6vE2wHF7V91czmcuYXcuPHhY4.


🧠⚛️ Beyond Penrose: Can Consciousness Be Derived from Geometry? For more than 30 years, Roger Penrose and Stuart Hameroff proposed that consciousness emerges through Objective Reduction (OR) inside neuronal microtubules. Penrose’s key equation is remarkably simple: τ_OR = ℏ / E_G where: τ_OR = collapse time ℏ = reduced Planck constant E_G = gravitational self-energy of the spacetime superposition The idea is: 🌌 Spacetime superposition ⟶ Gravitational instability ⟶ Wavefunction collapse ⟶ Conscious event But a major question remained: ❓ What is the mathematical mechanism that actually causes collapse? The EWOG framework attempts to provide one.

Maths is Cooked: AI’s Latest Breakthrough — And What’s Next

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As AI continues to improve its reasoning abilities, mathematicians are increasingly worried about the computer algorithms replacing them. In late May, those fears got even worse when OpenAI revealed that one of its general-purpose reasoning models had written a proof solving a math problem that’s sat unsolved for more than 80 years. But should they actually be worried? Let’s take a look.

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Google DeepMind AI Discovered a Mathematical Pattern Hidden in Prime Numbers

What exactly did DeepMind find?
Could this discovery help solve longstanding mathematical mysteries?
And what might it mean for cryptography, computing, and our understanding of mathematics itself?

In this video, we explore the science behind the discovery, the role of artificial intelligence in modern research, and why mathematicians around the world are paying close attention.

Whether this breakthrough leads to a revolutionary new theorem or simply a deeper understanding of prime numbers, it demonstrates the growing power of AI to accelerate scientific progress.

👇 What do YOU think?
Will AI help solve the greatest unsolved problems in mathematics?

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Most precise measurement of the force that binds nuclear matter achieved

Trinity’s Prof. Stefan Sint, along with collaborators from Germany, Spain and Italy, has published the most precise determination to date of the strong coupling constant. This parameter governs the interactions between quarks and gluons, the fundamental components of nuclear matter. The new result halves the error of all previous experimental measurements combined, setting a new benchmark for the Standard Model, which summarizes our current knowledge of elementary particle physics.

This advance will improve our understanding of how quarks and gluons behave inside protons and enable high-precision measurements of the Higgs boson and its properties. More generally, improved quantitative control of the strong interactions increases the likelihood of discovering effects of yet unknown physics at CERN’s Large Hadron Collider (LHC).

Prof. Sint from Trinity’s School of Mathematics was one of the researchers whose landmark results were published in Nature.

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