How Many Positive Coefficients Guarantee a Positive Modular Form?

Imagine a mathematical object, a modular form, whose coefficients are like the echoes of a hidden musical score. These coefficients, integers representing quantities from partitions to quadratic forms, are crucial to understanding the form’s deep mathematical structure. But what if, instead of carefully calculating each coefficient, we could establish that a modular form’s coefficients are…

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Can Vision-Language Models Hold a World in Mind?

On a sunlit afternoon, a team of researchers announced a quiet, ground‑level truth about the machines we’re increasingly inviting into our thought spaces: these systems can be surprisingly perceptive, and remarkably narrow. The study, a collaboration that sits at the crossroads of cognitive science and computer vision, emerges from Maitrix.org with contributors from UC San…

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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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A New Tensor Norm Quietly Reshapes Banach Spaces

Banach spaces are the mathematical playgrounds where infinity meets structure. They’re the kind of spaces that let you talk about convergence, continuity, and the delicate dance between algebra and analysis. For decades, researchers have tried to stitch together two such spaces into a single, coherent object called a tensor product. The reward would be a…

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When Echoes Lie Your Ears Find Truth

Untangling Voices from the Room’s Whisper We’ve all been there: a voice echoing off walls, turning crisp words into a muddled haze. Reverberation—the lingering echoes in a room—can make speech sound distant, muffled, or downright confusing. It’s the bane of clear communication, whether you’re on a video call, using voice assistants, or transcribing meetings. But…

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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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When Family Ties Break and Rewire the Social Web

Unraveling the Hidden Architecture of Family Networks Family is often described as the fundamental unit of society, a web of connections that shapes who we are and how we relate to the world. But beneath the surface of individual households lies a sprawling, intricate network of relationships stretching across generations. Understanding how this vast family…

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Could OTFS calm mmWave chaos across cells today?

The paper behind this piece isn’t about a single dazzling gadget or a flashy experiment. It’s about how the invisible plumbing of future wireless networks might work more gracefully when there are many cooks in the kitchen. In mmWave downlinks—those ultra-fast wireless links that promise mind-boggling data rates but hate getting blocked by a coffee…

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