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Archive for the ‘mathematics’ category: Page 22

Jun 12, 2023

The case for why our Universe may be a giant neural network

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

For example, scientists have recently emphasized that the physical organization of the Universe mirrors the structure of a brain. Theoretical physicist Sabine Hossenfelder — renowned for her skepticism — wrote a bold article for Time Magazine in August of 2022 titled “Maybe the Universe Thinks. Hear Me Out,” which describes the similarities. Like our nervous system, the Universe has a highly interconnected, hierarchical organization. The estimated 200 billion detectable galaxies aren’t distributed randomly, but lumped together by gravity into clusters that form even larger clusters, which are connected to one another by “galactic filaments,” or long thin threads of galaxies. When one zooms out to envision the cosmos as a whole, the “cosmic web” formed by these clusters and filaments looks strikingly similar to the “connectome,” a term that refers to the complete wiring diagram of the brain, which is formed by neurons and their synaptic connections. Neurons in the brain also form clusters, which are grouped into larger clusters, and are connected by filaments called axons, which transmit electrical signals across the cognitive system.

Hossenfelder explains that this resemblance between the cosmic web and the connectome is not superficial, citing a rigorous study by a physicist and a neuroscientist that analyzed the features common to both, and based on the shared mathematical properties, concluded that the two structures are “remarkably similar.” Due to these uncanny similarities, Hossenfelder speculates as to whether the Universe itself could be thinking.

Jun 12, 2023

A simple solution for nuclear matter in two dimensions

Posted by in categories: information science, mathematics, nuclear energy, particle physics, space

Understanding the behavior of nuclear matter—including the quarks and gluons that make up the protons and neutrons of atomic nuclei—is extremely complicated. This is particularly true in our world, which is three dimensional. Mathematical techniques from condensed matter physics that consider interactions in just one spatial dimension (plus time) greatly simplify the challenge.

Using this two-dimensional approach, scientists solved the complex equations that describe how low-energy excitations ripple through a system of dense nuclear matter. This work indicates that the center of stars, where such dense nuclear matter exists in nature, may be described by an unexpected form.

Being able to understand the quark interactions in two dimensions opens a new window into understanding neutron stars, the densest form of matter in the universe. The approach could help advance the current “golden age” for studying these exotic stars. This surge in research success was triggered by recent discoveries of gravitational waves and electromagnetic emissions in the cosmos.

Jun 12, 2023

A Quantum of Solace: Resolving a Mathematical Puzzle in Quarks and Gluons in Nuclear Matter

Posted by in categories: education, engineering, mathematics, particle physics

Scientists have taken a significant step forward in the study of the properties of quarks and gluons, the particles that make up atomic nuclei, by resolving a long-standing issue with a theoretical calculation method known as “axial gauge.” MIT

MIT is an acronym for the Massachusetts Institute of Technology. It is a prestigious private research university in Cambridge, Massachusetts that was founded in 1861. It is organized into five Schools: architecture and planning; engineering; humanities, arts, and social sciences; management; and science. MIT’s impact includes many scientific breakthroughs and technological advances. Their stated goal is to make a better world through education, research, and innovation.

Jun 12, 2023

UK hobbyist stuns math world with ‘amazing’ new shapes

Posted by in category: mathematics

David Smith, a retired print technician from the north of England, was pursuing his hobby of looking for interesting shapes when he stumbled onto one unlike any other in November.

When Smith shared his with the world in March, excited fans printed it onto T-shirts, sewed it into quilts, crafted cookie cutters or used it to replace the hexagons on a —some even made plans for tattoos.

The 13-sided polygon, which 64-year-old Smith called “the hat”, is the first single shape ever found that can completely cover an infinitely large flat surface without ever repeating the same pattern.

Jun 11, 2023

Unlocking Photonic Computing Power with Artificial ‘Life’

Posted by in categories: computing, encryption, food, mathematics, physics

Basic, or “elementary,” cellular automata like The Game of Life appeal to researchers working in mathematics and computer science theory, but they can have practical applications too. Some of the elementary cellular automata can be used for random number generation, physics simulations, and cryptography. Others are computationally as powerful as conventional computing architectures—at least in principle. In a sense, these task-oriented cellular automata are akin to an ant colony in which the simple actions of individual ants combine to perform larger collective actions, such as digging tunnels, or collecting food and taking it back to the nest. More “advanced” cellular automata, which have more complicated rules (although still based on neighboring cells), can be used for practical computing tasks such as identifying objects in an image.

Marandi explains: “While we are fascinated by the type of complex behaviors that we can simulate with a relatively simple photonic hardware, we are really excited about the potential of more advanced photonic cellular automata for practical computing applications.”

Marandi says cellular automata are well suited to photonic computing for a couple of reasons. Since information processing is happening at an extremely local level (remember in cellular automata, cells interact only with their immediate neighbors), they eliminate the need for much of the hardware that makes photonic computing difficult: the various gates, switches, and devices that are otherwise required for moving and storing light-based information. And the high-bandwidth nature of photonic computing means cellular automata can run incredibly fast. In traditional computing, cellular automata might be designed in a computer language, which is built upon another layer of “machine” language below that, which itself sits atop the binary zeroes and ones that make up digital information.

Jun 7, 2023

Mathematicians end decades-long quest to find elusive ‘vampire einstein’ shape

Posted by in category: mathematics

Researchers have discovered a new 14-sided shape called the Spectre that can be used to tile a surface without ever creating a repeating pattern, ending a decades’ long mathematical hunt.

Jun 6, 2023

If light has no mass, why is it affected by gravity? General Relativity Theory

Posted by in categories: information science, mathematics, space

General relativity, part of the wide-ranging physical theory of relativity formed by the German-born physicist Albert Einstein. It was conceived by Einstein in 1915. It explains gravity based on the way space can ‘curve’, or, to put it more accurately, it associates the force of gravity with the changing geometry of space-time. (Einstein’s gravity)

The mathematical equations of Einstein’s general theory of relativity, tested time and time again, are currently the most accurate way to predict gravitational interactions, replacing those developed by Isaac Newton several centuries prior.

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Jun 3, 2023

Joscha Bach: Time, Simulation Hypothesis, & Existence

Posted by in categories: cosmology, economics, education, government, information science, mathematics, quantum physics, robotics/AI

Joscha Bach is a cognitive scientist focusing on cognitive architectures, consciousness, models of mental representation, emotion, motivation and sociality.

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Jun 1, 2023

New links found between personality and cognitive abilities

Posted by in categories: mathematics, military, neuroscience

In a new landmark study, University of Minnesota research shows surprising links between human cognition and personality—pillars of human individuality that shape who we are and how we interact with the world. Personality influences our actions, emotions and thoughts, defining whether we are extroverted, polite, persistent, curious or anxious.

On the other hand, cognitive ability is the umbrella that reflects our capability for navigating complexity, such as articulating language, grasping intricate mathematics and drawing logical conclusions. Despite the prevailing belief that certain connections exist—for instance, introverted individuals are often perceived as more intelligent—scientists lacked a comprehensive understanding of these intricate connections.

The research, published in the Proceedings of the National Academy of Sciences, synthesizes data from over 1,300 studies from the past century, representing more than 2 million participants from 50 countries and integrating data from , test manuals, military databases, previously unpublished datasets and even proprietary databases of private companies.

Jun 1, 2023

Research team designs brain-inspired device for optoelectronic computing

Posted by in categories: information science, mathematics, robotics/AI

Perfect recall, computational wizardry and rapier wit: That’s the brain we all want, but how does one design such a brain? The real thing is comprised of ~80 billion neurons that coordinate with one another through tens of thousands of connections in the form of synapses. The human brain has no centralized processor, the way a standard laptop does.

Instead, many calculations are run in parallel, and outcomes are compared. While the operating principles of the human brain are not fully understood, existing mathematical algorithms can be used to rework deep learning principles into systems more like a human brain would. This brain-inspired computing paradigm—spiking (SNN)—provides a computing architecture well-aligned with the potential advantages of systems using both optical and .

In SNNs, information is processed in the form of spikes or action potentials, which are the that occur in real neurons when they fire. One of their key features is that they use asynchronous processing, meaning that spikes are processed as they occur in time, rather than being processed in a batch like in traditional neural networks. This allows SNNs to react quickly to changes in their inputs, and to perform certain types of computations more efficiently than traditional neural networks.

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