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Archive for the ‘mathematics’ category: Page 33

Dec 14, 2023

A Ball of Brain Cells on a Chip Can Learn Simple Speech Recognition and Math

Posted by in categories: mathematics, robotics/AI, supercomputing

The mini-brain functioned like both the central processing unit and memory storage of a supercomputer. It received input in the form of electrical zaps and outputted its calculations through neural activity, which was subsequently decoded by an AI tool.

When trained on soundbites from a pool of people—transformed into electrical zaps—Brainoware eventually learned to pick out the “sounds” of specific people. In another test, the system successfully tackled a complex math problem that’s challenging for AI.

The system’s ability to learn stemmed from changes to neural network connections in the mini-brain—which is similar to how our brains learn every day. Although just a first step, Brainoware paves the way for increasingly sophisticated hybrid biocomputers that could lower energy costs and speed up computation.

Dec 14, 2023

AI method for describing soft matter opens up new chapter in density functional theory

Posted by in categories: mathematics, physics, robotics/AI

“In the study, we demonstrate how artificial intelligence can be used to carry out fundamental theoretical physics that addresses the behavior of fluids and other complex soft matter systems,” says Prof. Dr. Matthias Schmidt, chair of Theoretical Physics II at the University of Bayreuth.


Scientists from Bayreuth have developed a new method for studying liquid and soft matter using artificial intelligence. In a study now published in the Proceedings of the National Academy of Sciences, they open up a new chapter in density functional theory.

We live in a highly technologized world where basic research is the engine of innovation, in a dense and complex web of interrelationships and interdependencies. The published research provides new methods that can have a great influence on widespread simulation techniques, so that complex substances can be investigated on computers more quickly, more precisely and more deeply.

Continue reading “AI method for describing soft matter opens up new chapter in density functional theory” »

Dec 14, 2023

Google’s New AI, Gemini, Beats ChatGPT In 30 Of 32 Test Categories

Posted by in categories: biotech/medical, ethics, law, mathematics, robotics/AI

Google has released a new Pro model of its latest AI, Gemini, and company sources say it has outperformed GPT-3.5 (the free version of ChatGPT) in widespread testing. According to performance reports, Gemini Ultra exceeds current state-of-the-art results on 30 of the 32 widely-used academic benchmarks used in large language model (LLM) research and development. Google has been accused of lagging behind OpenAI’s ChatGPT, widely regarded as the most popular and powerful in the AI space. Google says Gemini was trained to be multimodal, meaning it can process different types of media such as text, pictures, video, and audio.

Insider also reports that, with a score of 90.0%, Gemini Ultra is the first model to outperform human experts on MMLU (massive multitask language understanding), which uses a combination of 57 subjects such as math, physics, history, law, medicine and ethics for testing both world knowledge and problem-solving abilities.

The Google-based AI comes in three sizes, or stages, for the Gemini platform: Ultra, which is the flagship model, Pro and Nano (designed for mobile devices). According to reports from TechCrunch, the company says it’s making Gemini Pro available to enterprise customers through its Vertex AI program, and for developers in AI Studio, on December 13. Reports indicate that the Pro version can also be accessed via Bard, the company’s chatbot interface.

Dec 14, 2023

Mathematicians Prove the “Omniperiodicity” of Conway’s Game of Life

Posted by in categories: entertainment, mathematics

A problem that has long been a focal point of research for the famous Game of Life, has finally been solved.

Dec 13, 2023

P vs. NP: The Greatest Unsolved Problem in Computer Science

Posted by in categories: computing, information science, mathematics, science

Is it possible to invent a computer that computes anything in a flash? Or could some problems stump even the most powerful of computers? How complex is too complex for computation? The question of how hard a problem is to solve lies at the heart of an important field of computer science called computational complexity. Computational complexity theorists want to know which problems are practically solvable using clever algorithms and which problems are truly difficult, maybe even virtually impossible, for computers to crack. This hardness is central to what’s called the P versus NP problem, one of the most difficult and important questions in all of math and science.

This video covers a wide range of topics including: the history of computer science, how transistor-based electronic computers solve problems using Boolean logical operations and algorithms, what is a Turing Machine, the different classes of problems, circuit complexity, and the emerging field of meta-complexity, where researchers study the self-referential nature of complexity questions.

Continue reading “P vs. NP: The Greatest Unsolved Problem in Computer Science” »

Dec 12, 2023

Spinning up control: Propeller shape helps direct nanoparticles (w/video)

Posted by in categories: biotech/medical, chemistry, engineering, mathematics, nanotechnology

Self-propelled nanoparticles could potentially advance drug delivery and lab-on-a-chip systems — but they are prone to go rogue with random, directionless movements. Now, an international team of researchers has developed an approach to rein in the synthetic particles.

Led by Igor Aronson, the Dorothy Foehr Huck and J. Lloyd Huck Chair Professor of Biomedical Engineering, Chemistry and Mathematics at Penn State, the team redesigned the nanoparticles into a propeller shape to better control their movements and increase their functionality. They published their results in the journal Small (“Multifunctional Chiral Chemically-Powered Micropropellers for Cargo Transport and Manipulation”).

A propeller-shaped nanoparticle spins counterclockwise, triggered by a chemical reaction with hydrogen peroxide, followed by an upward movement, triggered by a magnetic field. The optimized shape of these particles allows researchers to better control the nanoparticles’ movements and to pick up and move cargo particles. (Video: Active Biomaterials Lab)

Dec 12, 2023

MIT mathematicians mimic ‘quantum bomb tester’ in droplet experiment

Posted by in categories: mathematics, particle physics, quantum physics

The experiment mirrored the principles of the quantum bomb tester, where a photon’s wave-particle behavior was theorized to detect the presence of a bomb without directly interacting with it.


A new study demonstrated how a droplet’s behavior imitates certain behaviors predicted for quantum particles — particularly photons.

Dec 12, 2023

Cyborg computer with living brain organoid aces machine learning tests

Posted by in categories: biotech/medical, cyborgs, mathematics, robotics/AI

Scientists have grown a tiny brain-like organoid out of human stem cells, hooked it up to a computer, and demonstrated its potential as a kind of organic machine learning chip, showing it can quickly pick up speech recognition and math predictions.

As incredible as recent advances have been in machine learning, artificial intelligence still lags way behind the human brain in some important ways. For example, the brain happily learns and adapts all day long on an energy budget of about 20 watts, where a comparably powerful artificial neural network needs about 8 million watts to achieve anything remotely comparable.

What’s more, the human brain’s neural plasticity, its ability to grow new nervous tissue and expand existing connective channels, has granted it an ability to learn from noisy, low-quality data streams, with minimal training and energy expenditure. What AI systems accomplish with brute force and massive energy, the brain achieves with an effortless elegance. It’s a credit to the billions of years of high-stakes trial and error that delivered the human brain to the state it’s in today, in which it’s chiefly used to watch vast numbers of other people dancing while we’re on the toilet.

Dec 11, 2023

The Intersection of Math and AI: A New Era in Problem-Solving

Posted by in categories: mathematics, robotics/AI

Conference is exploring burgeoning connections between the two fields.

Traditionally, mathematicians jot down their formulas using paper and pencil, seeking out what they call pure and elegant solutions. In the 1970s, they hesitantly began turning to computers to assist with some of their problems. Decades later, computers are often used to crack the hardest math puzzles. Now, in a similar vein, some mathematicians are turning to machine learning tools to aid in their numerical pursuits.

Embracing Machine Learning in Mathematics.

Dec 11, 2023

LeanDojo: Theorem Proving with Retrieval-Augmented Language Models

Posted by in categories: mathematics, robotics/AI

Lean Co-pilot for LLM-human collaboration to write formal mathematical proofs that are 100% accurate.


Top right: LeanDojo extracts proofs in Lean into datasets for training machine learning models. It also enables the trained model to prove theorems by interacting with Lean’s proof environment.

Top left: The proof tree of a Lean theorem ∀n∈N, gcd n n = n, where gcd is the greatest common divisor. When proving the theorem, we start from the original theorem as the initial state (the root) and repeatedly apply tactics (the edges) to decompose states into simpler sub-states, until all states are solved (the leaf nodes). Tactics may rely on premises such as mod_self and gcd_zero_left defined in a large math library. E.g., mod_self is an existing theorem ∀n∈N, n % n = 0 used in the proof to simplify the goal.

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