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Archive for the ‘mathematics’ category: Page 3

Dec 18, 2024

Physicists measure quantum geometry for first time

Posted by in categories: biotech/medical, mapping, mathematics, quantum physics, robotics/AI

Mapping the geometry of quantum worlds: measuring the quantum geometric tensor in solids.

Quantum states are like complex shapes in a hidden world, and understanding their geometry is key to unlocking the mysteries of modern physics. One of the most important tools for studying this geometry is the quantum geometric tensor (QGT). This mathematical object reveals how quantum states “curve” and interact, shaping phenomena ranging from exotic materials to groundbreaking technologies.

The QGT has two parts, each with distinct significance:

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Dec 18, 2024

The Dark Energy Pushing our Universe Apart may not be what it seems, scientists say

Posted by in categories: cosmology, mathematics

Distant, ancient galaxies are giving scientists more hints that a mysterious force called dark energy may not be what they thought.

Astronomers know that the universe is being pushed apart at an accelerating rate and they have puzzled for decades over what could possibly be speeding everything up. They theorize that a powerful, constant force is at play, one that fits nicely with the main mathematical model that describes how the universe behaves. But they can’t see it and they don’t know where it comes from, so they call it dark energy.

It is so vast it is thought to make up nearly 70% of the universe—while ordinary matter like all the stars and planets and people make up just 5%.

Dec 15, 2024

The Math Behind Neural Networks

Posted by in categories: mathematics, robotics/AI

Neural networks are at the core of artificial intelligence (AI), fueling a variety of applications from spotting objects in photos to translating languages. In this article, we’ll dive into what neural networks are, how they work, and why they’re a big deal in our technology-driven world today.

Index · 1: Understanding the Basics1.1: What are Neural Networks?1.2: Types of Neural Networks

· 2: The Architecture of Neural Networks2.1: The Structure of a Neuron2.2: Layers2.3: The Role of Layers in Learning.

Dec 14, 2024

Harvard Makes 1 Million Books Available to Train AI Models

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

Data is the new oil, as they say, and perhaps that makes Harvard University the new Exxon. The school announced Thursday the launch of a dataset containing nearly one million public domain books that can be used for training AI models. Under the newly formed Institutional Data Initiative, the project has received funding from both Microsoft and OpenAI, and contains books scanned by Google Books that are old enough that their copyright protection has expired.

Wired in a piece on the new project says the dataset includes a wide variety of books with “classics from Shakespeare, Charles Dickens, and Dante included alongside obscure Czech math textbooks and Welsh pocket dictionaries.” As a general rule, copyright protections last for the lifetime of the author plus an additional 70 years.

Foundational language models, like ChatGPT, that behave like a verisimilitude of a real human require an immense amount of high-quality text for their training—generally the more information they ingest, the better the models perform at imitating humans and serving up knowledge. But that thirst for data has caused problems as the likes of OpenAI have hit walls on how much new information they can find—without stealing it, at least.

Dec 14, 2024

Mathematicians Casually Discovered Two New Infinities

Posted by in category: mathematics

The possibilities might be endless—literally.

Dec 13, 2024

Identification of the Potential Molecular Mechanisms Linking RUNX1 Activity with Nonalcoholic Fatty Liver Disease, by Means of Systems Biology

Posted by in categories: biotech/medical, mathematics

📝 — Bertran, et al.

Full text is available 👇


Nonalcoholic fatty liver disease (NAFLD) is the most prevalent chronic hepatic disease; nevertheless, no definitive diagnostic method exists yet, apart from invasive liver biopsy, and nor is there a specific approved treatment. Runt-related transcription factor 1 (RUNX1) plays a major role in angiogenesis and inflammation; however, its link with NAFLD is unclear as controversial results have been reported. Thus, the objective of this work was to determine the proteins involved in the molecular mechanisms between RUNX1 and NAFLD, by means of systems biology. First, a mathematical model that simulates NAFLD pathophysiology was generated by analyzing Anaxomics databases and reviewing available scientific literature.

Dec 13, 2024

Max Tegmark: Will AI Surpass Human Intelligence?

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

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Will AI ever surpass human intelligence, discover new laws of physics, and solve the greatest mysteries of our universe?

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Dec 12, 2024

Welcome to The Quantum Memory Matrix — Hypothesis Offers New Insight Into Black Hole Information Paradox

Posted by in categories: computing, cosmology, mathematics, quantum physics

A new hypothesis suggests that the very fabric of space-time may act as a dynamic reservoir for quantum information, which, if it holds, would address the long-standing Black Hole Information Paradox and potentially reshape our understanding of quantum gravity, according to a research team including scientists from pioneering quantum computing firm, Terra Quantum and Leiden University.

Published in Entropy, the Quantum Memory Matrix (QMM) hypothesis offers a mathematical framework to reconcile quantum mechanics and general relativity while preserving the fundamental principle of information conservation.

The study proposes that space-time, quantized at the Planck scale — a realm where the physics of quantum mechanics and general relativity converge — stores information from quantum interactions in “quantum imprints.” These imprints encode details of quantum states and their evolution, potentially enabling information retrieval during black hole evaporation through mechanisms like Hawking radiation. This directly addresses the Black Hole Information Paradox, which highlights the conflict between quantum mechanics — suggesting information cannot be destroyed — and classical black hole descriptions, where information appears to vanish once the black hole evaporates.

Dec 12, 2024

Mathematician solves the moving sofa problem

Posted by in category: mathematics

A mathematician at Yonsei University, in Korea, claims to have solved the moving sofa problem. Jineon Baek has posted a 100+-page proof of the problem on the arXiv preprint server.

Most people who have moved their place of residence have encountered the moving sofa problem—it comes up when attempting to carry a couch around a corner. What is the largest couch that can be carried around a given corner without getting stuck? This problem was posited mathematically by Leo Moser back in 1966, and until now, has remained unsolved.

Moser’s initial thoughts centered on the possibility of developing a proof showing how mathematics could be used to solve any such problem using a given shape of a plane as it was moved around a right-angled corner of an empty space (such as a hallway) that was one unit in width.

Dec 11, 2024

Death Isn’t Final: New Math Model Suggests Cells Can Be Revived

Posted by in categories: biotech/medical, mathematics

Cellular death is a fundamental concept in biological sciences. Despite its importance, its definition varies depending on the context in which it occurs and lacks a general mathematical definition.

Researchers from the University of Tokyo propose a new mathematical definition of death based on whether a potentially dead cell can return to a predefined “representative state of living,” which are the states of being that we can confidently call “alive.” The researchers’ work could be useful for biological researchers and future medical research.

While it’s not something we like to think about, death comes for us all eventually, whether you’re an animal, a plant, or even a cell. And even though we can all differentiate between what is alive and dead, it might be surprising to know that death at a cellular level lacks a widely recognized mathematical definition.

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