The study shows that if a matrix filled with 0s and 1s has either a small γ₂‑norm or a small normalized trace norm, it must hide a large square of all 1s or all 0s. This confirms a claim made by Hambardzumyan, Hatami, and Hatami. The researchers also explore other patterns that arise when Boolean ma
The U. S. Constitution says anyone born on American soil and under its flag is a citizen, no matter who their parents are. This rule does not care about race, gender, religion, or whether the parents are U. S. citizens. It simply looks at where a baby is born and that the country’s flag is abo
Tiny language models can turn long health articles into short, clear summaries that help keep hospitals honest. Because the medical world mixes public and private work, many people, and global suppliers, it is easy for fraud to sneak in. Large bills, hidden costs, and uneven information make i
A heavy snowstorm hit the northeast on Monday, sending huge amounts of fresh ice and wind into city streets. The weather followed a previous storm that had left some melted snow behind, but new drifts quickly covered roads and parking lots. As a result, authorities in states from Delaware to Massach
The new office for Imabari Shipbuilding’s Marugame site was finished in 2025. It covers 8, 489 square metres and is located on a former industrial plot that once stretched over 0. 88 km². Architects Yano Toshihiro and Eriko Aoyama, working with designer Rin Nishikawa, saw a chance to bring together
Bitcoin’s safety is built on a type of math called ECDSA that current computers cannot crack. Some experts think that once powerful quantum machines exist, they could pull private keys from public ones once those public keys appear on the blockchain. If that happens, any coin whose public key is alr
Medical students often learn about kids and teens with mental health problems. Two ways of training are compared: a computer‑based virtual reality tool and the old method where students talk to actual patients. The study looks at what each approach does well and where it falls short. First, the vir
Over 80 artists who have been part of the Berlin Film Festival have signed a public letter. They want the festival to speak clearly about the war in Gaza. The letter was published in Variety, a magazine for the entertainment industry. It asks the festival to oppose what it calls Israel's genocide an
Morgan Stanley Investment Management has just wrapped up a big deal. They created a special fund called MSABF 2026-1. This fund is all about consumer loans. It's backed by loans from different top lenders. The fund is rated by a well-known agency, KBRA. It has a revolving structure, which means it c
In 2017, a chance meeting with Jeff Bezos left a lasting impression. Sitting at a dinner in Italy, the owner of the Washington Post spoke passionately about investing in journalism. He promised to grow the newsroom and turn the paper around. At the time, this was encouraging news. Many media outlets
