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Category: mathematics – Page 7

In a ground-breaking theoretical study, two physicists have identified a new class of quasiparticle called the paraparticle. Their calculations suggest that paraparticles exhibit quantum properties that are fundamentally different from those of familiar bosons and fermions, such as photons and electrons respectively.

Using advanced mathematical techniques, Kaden Hazzard at Rice University in the US and his former graduate student Zhiyuan Wang, now at the Max Planck Institute of Quantum Optics in Germany, have meticulously analysed the mathematical properties of paraparticles and proposed a real physical system that could exhibit paraparticle behaviour.

“Our main finding is that it is possible for particles to have exchange statistics different from those of fermions or bosons, while still satisfying the important physical principles of locality and causality,” Hazzard explains.

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Mathematics and physics have long been regarded as the ultimate languages of the universe, but what if their structure resembles something much closer to home: our spoken and written languages? A recent study suggests that the mathematical equations used to describe physical laws follow a surprising pattern—a pattern that aligns with Zipf’s law, a principle from linguistics.

This discovery could reshape our understanding of how we conceptualize the universe and even how our brains work. Let’s explore the intriguing connection between the language of mathematics and the physical world.

What Is Zipf’s Law?

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Yale physicists have discovered a sophisticated, previously unknown set of “modes” within the human ear that put important constraints on how the ear amplifies faint sounds, tolerates noisy blasts, and discerns a stunning range of sound frequencies in between.

By applying existing mathematical models to a generic mock-up of a cochlea—a spiral-shaped organ in the inner ear—the researchers have revealed a new layer of cochlear complexity. The findings, which appear in PRX Life, offer fresh insight into the remarkable capacity and accuracy of human hearing.

“We set out to understand how the ear can tune itself to detect faint sounds without becoming unstable and responding even in the absence of external sounds,” said Benjamin Machta, an assistant professor of physics in Yale’s Faculty of Arts and Science and co-senior author of the new study. “But in getting to the bottom of this we stumbled onto a new set of low frequency mechanical modes that the cochlea likely supports.”

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In today’s AI news, Mukesh Ambani’s Reliance Industries is set to build the world’s largest data centre in Jamnagar, Gujarat, according to a *Bloomberg News* report. The facility would dwarf the current largest data center, Microsoft’s 600-megawatt site in Virginia. The project could cost between $20 billion to $30 billion.

S most popular consumer-facing AI app. The Beijing-based company introduced its closed-source multimodal model Doubao 1.5 Pro, emphasizing a “resource-efficient” training approach that it said does not sacrifice performance. ‘ + And, OpenAI’s CEO Sam Altman announced that the free tier of ChatGPT will now use the o3-mini model, marking a significant shift in how the popular AI chatbot serves its user base. In the same tweet announcing the change, Altman revealed that paid subscribers to ChatGPT Plus and Pro plans will enjoy “tons of o3-mini usage,” giving people an incentive to move to a paid account with the company.

Then, researchers at Sakana AI, an AI research lab focusing on nature-inspired algorithms, have developed a self-adaptive language model that can learn new tasks without the need for fine-tuning. Called Transformer², the model uses mathematical tricks to align its weights with user requests during inference.

In videos, Demis Hassabis, CEO of Google DeepMind joins the Big Technology Podcast with Alex Kantrowitz to discuss the cutting edge of AI and where the research is heading. In this conversation, they cover the path to artificial general intelligence, how long it will take to get there, how to build world models, and much more.

Squawk Box Then, join IBM’s Meredith Mante as she takes you on a deep dive into Lag Llama, an open-source foundation model, and shows you how to harness its power for time series forecasting. Learn how to load and preprocess data, train a model, and evaluate its performance, gaining a deeper understanding of how to leverage Lag Llama for accurate predictions.

We close out with, CEO Sam Altman, along with OpenAI researchers and developers, Yash Kumar, Casey Chu, and Reiichiro Nakano as they introduce and demonstrate Operator, the new computer-user AI Agent from OpenAI.

Thats all for today, but AI is moving fast, subscribe today to stay informed. Please don’t forget to vote for me in the Entrepreneur of Impact Competition today! Thank you for supporting me and my partners, it’s how I keep NNN free.

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Cool biophysical modeling of the endoplasmic reticulum!

Active liquid network [ https://www.czbiohub.org/life-science/a-simple-model-for-an-…structure/](https://www.czbiohub.org/life-science/a-simple-model-for-an-…structure/)

Scientists use math and physics to address the mystery of just how the endoplasmic reticulum, an organelle essential to life at the cellular level, continually re-arranges itself.

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Up until last week, physicists believed that matter is made up of only two types of particles: those whose spin has full-integer values (bosons) and those whose spin comes has half-integer values (fermions). But in a new paper, a group of researchers turned the world of physics upside down by mathematically proving that a third type of particles – the “paraparticles” are possible.

Paper: https://www.nature.com/articles/s4158…

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The challenge for researchers is to develop the often complicated series of equations that are needed to describe these phenomena and ensure that they can be solved to recover information on the location of the objects over time. Often the systems of equations needed to describe such phenomena are based on partial differential equations: the series of equations that describe the location and time-evolution of a system are known as a distributed parameter system.

Mathematical models can help us not just understand historical behaviour but predict where the smoke particles will spread next.

Professor Francisco Jurado at the Tecnológico Nacional de México has been working on approaches to solve the problem of distributed parameter systems to describe diffusion–convection systems. He has recently developed an approach using a combination of approaches, including the Sturm-Liouville differential operator and the regulator problem, to develop a model for diffusion–convection behaviour that is sufficiently stable and free of external disturbances. Importantly, this approach allows us to yield meaningful information for real systems.

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Most of us assume reality is made up of physical matter. In line with this, scientists have built ever larger machines to identify the ultimate particles. Instead of getting closer to the most elementary bits in the universe, the particle zoo has got ever more complex and seemingly less like material stuff at all. Is there a danger that the very idea of an ultimate foundation to reality is a profound mistake? Some have proposed that instead of material, the ultimate foundation is to be found in consciousness, information, or even mathematics. But such proposals are no closer to identifying ultimate elements than particle physicists. Should we give up the attempt to uncover an ultimate foundation to the universe? Is our inability to find an ultimate foundation a limitation of language, or of our capacity to make sense of the world, or is it to do with the nature of reality itself?

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