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Category: mathematics

New formula improves accuracy of particle concentration measurements in diverse samples

Researchers can use a metric called the particle number concentration (PNC) to calculate the number of particles in a sample, such as the number of marbles in a jar.

Researchers at the National Institute of Standards and Technology (NIST) have developed a new mathematical formula to calculate the concentration of particles suspended in a solution. The new approach, which yields more accurate results than current methods, can be used to deliver the correct drug dosage to patients, measure the amount of nanoplastics in , and help ensure the correct level of additives in , among other applications.

The researchers have published their findings in Analytical Chemistry.

Falling water forms beautiful fluted films

When water drains from the bottom of a vertical tube, it is followed by a thin film of liquid that can adopt complex and beautiful shapes. KAUST researchers have now studied exactly how these “fluted films” form and break up, developing a mathematical model of their behavior that could help improve the performance, safety, and efficiency of industrial processes.

Mathematical model reveals how collapsing matter and expanding voids shape universe’s evolution

A University of Queensland researcher has developed a new mathematical model to explain the evolution of the universe which, for the first time, includes collapsing regions of matter and expanding voids.

Physicists create stable, ‘breathing’ solitons in settings without energy conservation

Solitonic waves—waves that keep their shape and direction of motion for a long time—have intrigued physicists for almost two centuries. In real-world circumstances, these waves eventually die out due to energy loss. A team of UvA physicists have now discovered how a particular type of interaction can be used to create very stable solitons, even in circumstances where energy is not conserved.

In 1834, John Scott Russell observed an unusual phenomenon in the Union Canal in Scotland. After a moving boat had come to a halt, the water wave that the boat had caused continued moving through the canal, keeping virtually the same speed and the same shape.

It took more than half a century, until the work of Dutch mathematicians Diederik Korteweg and Gustav de Vries in 1895, before the phenomenon that Russell observed had been explained in all its mathematical detail. What Russell had seen was a “solitary wave,” a phenomenon now better known as a soliton.

Tesla Kills Dojo for AI6! Here’s Why

Questions to inspire discussion.

🚗 Q: How will AI6 be used in Tesla vehicles? A: AI6 will be used for FSD inference, with two chips in every car, enabling advanced autonomous driving capabilities.

🤖 Q: What role will AI6 play in Optimus? A: AI6 will enable on-device learning and reinforced learning in Optimus, enhancing its AI capabilities.

🔋 Q: Will AI6 be used in other Tesla products? A: AI6 will be integrated into every edge device produced by Tesla, including Tesla Semi, Mega Pack, and security cameras.

Technical Specifications.

💻 Q: What is the architecture of AI6? A: AI6 will use a cluster model of individual chips with a software layer on top, similar to Dojo 3 for training.

Continue reading “Tesla Kills Dojo for AI6! Here’s Why” | >

This “smart coach” helps LLMs switch between text and code

Large language models (LLMs) excel at using textual reasoning to understand the context of a document and provide a logical answer about its contents. But these same LLMs often struggle to correctly answer even the simplest math problems.

Textual reasoning is usually a less-than-ideal way to deliberate over computational or algorithmic tasks. While some LLMs can generate code like Python to handle symbolic queries, the models don’t always know when to use code, or what kind of code would work best.

LLMs, it seems, may need a coach to steer them toward the best technique.

Enter CodeSteer, a smart assistant developed by MIT researchers that guides an LLM to switch between code and text generation until it correctly answers a query. (Strangely like a text editor “CodeSteer”🤔)

CodeSteer is a smart assistant from MIT that automatically guides large language models to switch between generating text and code, and to refine its response, until it answers a query correctly.

Using sound to remember quantum information 30 times longer

While conventional computers store information in the form of bits, fundamental pieces of logic that take a value of either 0 or 1, quantum computers are based on qubits. These can have a state that is simultaneously both 0 and 1. This odd property, a quirk of quantum physics known as superposition, lies at the heart of quantum computing’s promise to ultimately solve problems that are intractable for classical computers.

Many existing quantum computers are based on superconducting electronic systems in which electrons flow without resistance at extremely low temperatures. In these systems, the quantum mechanical nature of electrons flowing through carefully designed resonators creates superconducting qubits.

These qubits are excellent at quickly performing the logical operations needed for computing. However, storing information—in this case quantum states, mathematical descriptors of particular quantum systems—is not their strong suit. Quantum engineers have been seeking a way to boost the storage times of quantum states by constructing so-called “quantum memories” for superconducting qubits.

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