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Category: mathematics – Page 18

Researchers provide mathematical solutions to study 2D light interaction in photonic crystal lasers

Laser diodes are semiconductors that generate light and amplify it using repeated reflection or “optical feedback.” Once the light has achieved desirable optical gain, laser diodes release it as powerful laser beams.

Photonic crystal surface-emitting lasers (PCSELs) are advanced where the optical gain is typically distributed laterally to the propagating light within a photonic crystal (PC) structure. They differ from traditional lasers by separating gain, feedback, and emission functions, offering scalable single-mode power and innovative designs. This leads to enhanced performance and new application possibilities.

In a paper that was published in the IEEE Journal of Selected Topics in Quantum Electronics on 20 November 2024, researchers have developed a method to numerically simulate the interaction of light waves within PCSELs.

Groundbreaking tachyon discovery brings time travel closer to reality

A theoretical particle that travels faster than light, the tachyon has long intrigued physicists and fueled decades of speculation. Initially conceived as a possible solution to quantum and relativity paradoxes, tachyons remain purely hypothetical. Despite the lack of experimental evidence, they continue to serve as a thought-provoking concept in modern physics.

A recent study by an international team of researchers has reignited interest in tachyons, suggesting they might be possible within the framework of Einstein’s special theory of relativity. This bold claim challenges conventional understandings of causality and time, raising fundamental questions about the structure of reality. If confirmed, it could lead to a radical shift in how scientists perceive the limits of physical laws.

Physicist Gerald Feinberg introduced the idea of tachyons in 1962, proposing that such particles could always travel faster than light without ever slowing down to subluminal speeds. His argument was based on the concept of imaginary mass, a theoretical construct involving the square root of a negative number. This allowed for the mathematical possibility of faster-than-light motion without explicitly violating relativity.

Neuroscientists crack the code of how we make decisions with new mathematical framework

A new mathematical model sheds light on how the brain processes different cues, such as sights and sounds, during decision making. The findings from Princeton neuroscientists may one day improve how brain circuits go awry in neurological disorders, such as Alzheimer’s, and could help artificial brains, like Alexa or self-driving car technology, more helpful.

DeepMind AI achieves gold-medal level performance on challenging Olympiad math questions

A team of researchers at Google’s DeepMind project, reports that its AlphaGeometry2 AI performed at a gold-medal level when tasked with solving problems that were given to high school students participating in the International Mathematical Olympiad (IMO) over the past 25 years. In their paper posted on the arXiv preprint server, the team gives an overview of AlphaGeometry2 and its scores when solving IMO problems.

Prior research has suggested that AI that can solve geometry problems could lead to more sophisticated apps because they require both a high level of reasoning ability and an ability to choose from possible steps in working toward a solution to a problem.

To that end, the team at DeepMind has been working on developing increasingly sophisticated geometry-solving apps. Its first iteration was released last January and was called AlphaGeometry; its second iteration is called AlphaGeometry2.

DeepMind claims its AI performs better than International Mathematical Olympiad gold medalists

An AI system developed by Google DeepMind, Google’s leading AI research lab, appears to have surpassed the average gold medalist in solving geometry problems in an international mathematics competition.

The system, called AlphaGeometry2, is an improved version of a system, AlphaGeometry, that DeepMind released last January. In a newly published study, the DeepMind researchers behind AlphaGeometry2 claim their AI can solve 84% of all geometry problems over the last 25 years in the International Mathematical Olympiad (IMO), a math contest for high school students.

Why does DeepMind care about a high-school-level math competition? Well, the lab thinks the key to more capable AI might lie in discovering new ways to solve challenging geometry problems — specifically Euclidean geometry problems.

Generalizing Safety Beyond Collision-Avoidance via Latent-Space Reachability Analysis

Hamilton-Jacobi (HJ) reachability is a rigorous mathematical framework that enables robots to simultaneously detect unsafe states and generate actions that prevent future failures. While in theory, HJ reachability can synthesize safe controllers for nonlinear systems and nonconvex constraints.

In practice, it has been limited to hand-engineered collision

Avoidance constraints modeled via low-dimensional state-space representations and first-principles dynamics. In this work, our goal is to generalize safe robot controllers to prevent failures that are hard—if not impossible—to write down by hand, but can be intuitively identified from high-dimensional observations:

Google Launches Gemini 2.0 Pro LLM

In today’s AI news, Google launched its much-anticipated new flagship AI model, Gemini 2.0 Pro Experimental, on Wednesday. The announcement was part of a series of other AI model releases. The company is also making its reasoning model, Gemini 2.0 Flash Thinking, available in the Gemini app.

In other advancements, LinkedIn is testing a new job-hunting tool that uses a custom large language model to comb through huge quantities of data to help people find prospective roles. The company believes that artificial intelligence will help users unearth new roles they might have missed in the typical search process.

S Deep Research feature, which can autonomously browse the web and create research reports. ‘ + s up from hitting $50 million ARR, or the yearly value of last month s case for why they are the best positioned to take over TikTok And, in this episode, a16z Partner Marc Andrusko chats with Mastercard’s Chief AI and Data Officer Greg Ulrich about Mastercard’s long history of using AI, the opportunities (and potential risks) associated with integrating generative AI into fraud detection, determining what tech to employ based on use cases, and the best advice he’s ever gotten.

Then, power your AI transformation with an insightful keynote from Scott Guthrie, Executive Vice President, Cloud + AI Group at Microsoft, and other industry experts. Watch this keynote presentation from NYC stop on Microsoft’s AI Tour.

We close out with this insightful discussion with Malcolm Gladwell and Ric Lewis, SVP of Infrastructure at IBM. Learn how hardware capabilities enable the matrix math behind large language models and how AI is transforming industries—from banking to your local coffee shop.

Thats all for today, but AI is moving fast — like, comment, and subscribe for more AI news! Please vote for me in the Entrepreneur of Impact Competition today! Thank you for supporting my partners and I — it’s how I keep Neural News Network free.

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New AI Tool Detects Fake News with 99% Accuracy

A tool developed by Keele University researchers has been shown to help detect fake news with an impressive 99% level of accuracy, offering a vital resource in combating online misinformation.

The researchers Dr. Uchenna Ani, Dr. Sangeeta Sangeeta, and Dr. Patricia Asowo-Ayobode from Keele’s School of Computer Science and Mathematics, used a number of different machine learning techniques to develop their model, which can scan news content to give a judgment of whether a news source is trustworthy and genuine or not.

The method developed by the researchers uses an “ensemble voting” technique, which combines the predictions of multiple different machine learning models to give an overall score.