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Researchers report a new, highly unusual, structured-light family of 3D topological solitons, the photonic hopfions, where the topological textures and topological numbers can be freely and independently tuned.

We can frequently find in our daily lives a localized wave structure that maintains its shape upon propagation—picture a smoke ring flying in the air. Similar stable structures have been studied in various research fields and can be found in magnets, nuclear systems, and particle physics. In contrast to a ring of smoke, they can be made resilient to perturbations. This is known in mathematics and physics as topological protection.

A typical example is the nanoscale hurricane-like texture of a magnetic field in magnetic thin films, behaving as particles—that is, not changing their shape—called skyrmions. Similar doughnut-shaped (or toroidal) patterns in 3D space, visualizing complex spatial distributions of various properties of a wave, are called hopfions. Achieving such structures with light waves is very elusive.

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We can frequently find in our daily lives a localized wave structure that maintains its shape upon propagation—picture a smoke ring flying in the air. Similar stable structures have been studied in various research fields and can be found in magnets, nuclear systems, and particle physics. In contrast to a ring of smoke, they can be made resilient to perturbations. This is known in mathematics and physics as topological protection.

A typical example is the nanoscale hurricane-like texture of a magnetic field in magnetic thin films, behaving as particles—that is, not changing their shape—called skyrmions. Similar doughnut-shaped (or toroidal) patterns in 3D space, visualizing complex spatial distributions of various properties of a wave, are called hopfions. Achieving such structures with light waves is very elusive.

Recent studies of structured light revealed strong spatial variations of polarization, phase, and amplitude, which enable the understanding of—and open up opportunities for designing—topologically stable optical structures behaving like particles. Such quasiparticles of light with control of diversified topological properties may have great potential, for example as next-generation information carriers for ultra-large-capacity optical information transfer, as well as in quantum technologies.

Mathematicians came up with the first examples of intransitive dice more than 50 years ago, and eventually proved that as you consider dice with more and more sides, it’s possible to create intransitive cycles of any length. What mathematicians didn’t know until recently was how common intransitive dice are. Do you have to contrive such examples carefully, or can you pick dice randomly and have a good shot at finding an intransitive set?

Looking at three dice, if you know that A beats B and B beats C, that seems like evidence that A is the strongest; situations where C beats A should be rare. And indeed, if the numbers on the dice are allowed to add up to different totals, then mathematicians believe that this intuition holds true.

But a paper posted online late last year shows that in another natural setting, this intuition fails spectacularly. Suppose you require that your dice use only the numbers that appear on a regular die and have the same total as a regular die. Then, the paper showed, if A beats B and B beats C, A and C have essentially equal chances of prevailing against each other.

In the world of spreadsheets and data analysis, a new player has emerged to shake up the game. Akkio, the easy-to-use AI company, has launched Chat Data Prep, a revolutionary machine learning platform that allows users to transform data using ordinary conversational language.

Gone are the days of struggling with complicated formulas and formatting commands in Excel. With Akkio’s Chat Data Prep, users can simply type in conversational language to make changes to their spreadsheet data. Leveraging AI and large language models, the platform interprets the user’s requests and makes the necessary changes to the data.

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ChatGPT was hailed as one of 2022’s most impressive technological innovations upon its release last November. The powerful artificial intelligence (AI) chatbot can generate text on almost any topic or theme, from a Shakespearean sonnet reimagined in the style of Megan Thee Stallion, to complex mathematical theorems described in language a 5 year old can understand. Within a week, it had more than a million users.

ChatGPT’s creator, OpenAI, is now reportedly in talks with investors to raise funds at a $29 billion valuation, including a potential $10 billion investment by Microsoft. That would make OpenAI, which was founded in San Francisco in 2015 with the aim of building superintelligent machines, one of the world’s most valuable AI companies.

But the success story is not one of Silicon Valley genius alone. In its quest to make ChatGPT less toxic, OpenAI used outsourced Kenyan laborers earning less than $2 per hour, a TIME investigation has found.

In this video, we will attempt to solve a mixed case concerning #absolute #value #inequality for you, and then the results will be applied to a real domain, with surprising outcomes.
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A new study led by scientists at Rutgers University has uncovered new insights into the underlying brain mechanisms of autism spectrum disorder.

Autism Spectrum Disorder (ASD) is a complex developmental disorder that affects how a person communicates and interacts with others. It is characterized by difficulty with social communication and interaction, as well as repetitive behaviors and interests. ASD can range from mild to severe, and individuals with ASD may have a wide range of abilities and challenges. It is a spectrum disorder because the symptoms and characteristics of ASD can vary widely from person to person. Some people with ASD are highly skilled in certain areas, such as music or math, while others may have significant learning disabilities.

Still, Larsen’s most recent obsession felt different, “longer and more intense than most of his other projects,” she said. For more than a year and a half, Larsen couldn’t stop thinking about a certain math problem.

Then, in November 2021, Granville opened up an email from Larsen, then 17 years old and in his senior year of high school. A paper was attached — and to Granville’s surprise, it looked correct. “It wasn’t the easiest read ever,” he said. “But when I read it, it was quite clear that he wasn’t messing around. He had brilliant ideas.”

Pomerance, who read a later version of the work, agreed. “His proof is really quite advanced,” he said. “It would be a paper that any mathematician would be really proud to have written. And here’s a high school kid writing it.”

Continue reading “Teenager Solves Stubborn Riddle About Prime Number Look-Alikes” »