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[:es]Mathematicians Discover the Fibonacci Numbers Hiding in Strange Spaces[:]

[:es]Recent explorations of unique geometric worlds reveal perplexing patterns, including the Fibonacci sequence and the golden ratio.[:]
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[:es]Teenager Solves Stubborn Riddle About Prime Number Look-Alikes[:]

[:es]In his senior year of high school, Daniel Larsen proved a key theorem about Carmichael numbers — strange entities that mimic the primes. “It would be a paper that any […]
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[:es]‘Monumental’ Math Proof Solves Triple Bubble Problem and More[:]

[:es]The decades-old Sullivan’s conjecture, about the best way to minimize the surface area of a bubble cluster, was thought to be out of reach for three bubbles and up — […]
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[:es]Biologists Use Genetic Circuits to Program Plant Roots[:]

[:es]Using inserted genetic circuitry, synthetic biologists controlled the growth of plant roots for the first time.[:]
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[:es]High-Temperature Superconductivity Understood at Last[:]

[:es]A new atomic-scale experiment all but settles the origin of the strong form of superconductivity seen in cuprate crystals, confirming a 35-year-old theory.[:]
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[:es]How Do Fireflies Flash in Sync? Studies Suggest a New Answer[:]

[:es]Field research suggests a new explanation for the synchronized flashing in fireflies and confirms that a novel form of “chimeric” synchrony occurs naturally.[:]
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[:es]Chaos Researchers Can Now Predict Perilous Points of No Return[:]

[:es]A custom-built machine learning algorithm can predict when a complex system is about to switch to a wildly different mode of behavior.[:]
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[:es]How Transformers Seem to Mimic Parts of the Brain[:]

[:es]Neural networks originally designed for language processing turn out to be great models of how our brains understand places. [:]
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[:es]How Shannon Entropy Imposes Fundamental Limits on Communication[:]

[:es]What’s a message, really? Claude Shannon recognized that the elemental ingredient is surprise.[:]