A Fresh Rule for Fair Islamic Profit Sharing

In the business of Islamic finance, a quiet revolution is taking shape not in the form of flashy new instruments, but in a smarter way to distribute profits when two or more parties join forces. A team of researchers from ENSIIE and the Laboratoire de Mathématiques et Modélisation d’Evry (LaMME) at Université Évry Paris-Saclay has…

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Hidden Black Holes Shape the X-ray Sky’s Glow

The cosmic X-ray background is the faint, diffuse glow that blankets the sky in X-rays, a celestial sunrise stitched together from the hearts of galaxies. Most of that glow comes from active galactic nuclei, the hungry cores of galaxies where matter rushes into supermassive black holes and their violent appetites fuel light across the spectrum….

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When Numbers Refuse to Align How Weighted Approximations Rewrite Math’s Rules

The Puzzle of Perfect Approximation At the heart of mathematics lies a deceptively simple question: how well can we approximate real numbers by rational ones? This question, which echoes through centuries of mathematical thought, is the essence of Diophantine approximation. It’s about finding integer solutions that come tantalizingly close to hitting a target defined by…

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AI’s New Test: Can It Master Your Computer?

The digital world is a chaotic symphony of clicking, scrolling, and typing. We navigate it effortlessly, yet for artificial intelligence, even the simplest tasks can feel like scaling Mount Everest. A team of researchers from Shanghai Jiao Tong University, Xiamen University, the University of Science and Technology of China, and other leading institutions across China…

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Could AI Learn to Pentest Web Apps on Its Own?

Intro Cybersecurity often feels like a high-stakes game of chess played on a sprawling, ever-changing board. Defenders patch holes, monitor traffic, and chase down elusive weaknesses, while attackers scout for the tiniest misstep to exploit. For decades, penetration testing has been a human-led craft: security experts map a network, probe forms, test credentials, and chase…

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The Hidden Motives Behind Coherent Spaces

The Hidden Motives Behind Coherent Spaces Georg Lehner’s new work on algebraic K-theory of coherent spaces invites readers to meet a surprising team: abstract spaces that look tiny on the surface, yet encode wild arithmetic below. The central claim is deceptively simple: to understand deep invariants of categories of sheaves on these spaces, you might…

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Do Singular Matrices Harbor a Hidden Rule?

The world of matrices is a world of rules that stubbornly resist cramming into a single sentence. A team of mathematicians from the University at Buffalo and the University of Zagreb has asked a deceptively simple question about those rules: what happens when you squeeze the spectrum of a matrix and demand that certain structural…

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AI Learns to ‘See’ Through Clouds: A New Dataset for Synthetic Aperture Radar

Peering Through the Haze: The Promise of Synthetic Aperture Radar Synthetic Aperture Radar (SAR) is a remarkable technology. Unlike ordinary cameras that rely on visible light, SAR uses radio waves to create images. This means it can ‘see’ through clouds, rain, and even darkness—a game-changer for everything from disaster response to mapping remote regions. But…

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