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Archive for the ‘mathematics’ category: Page 84

May 30, 2022

Physicists Discover Strange Array of Links and Knots in Quantum Matter

Posted by in categories: climatology, mathematics, quantum physics

As physicists dig deeper into the quantum realm, they are discovering an infinitesimally small world composed of a strange and surprising array of links, knots, and winding. Some quantum materials exhibit magnetic whirls called skyrmions — unique configurations sometimes described as “subatomic hurricanes.” Others host a form of superconductivity that twists into vortices.

Now, in an article published in the journal Nature, a Princeton-led team of scientists has discovered that electrons in quantum matter can link one another in strange new ways. The work brings together ideas in three areas of science – condensed matter physics, topology, and knot theory – in a new way, raising unexpected questions about the quantum properties of electronic systems.

Topology is the branch of theoretical mathematics that studies geometric properties that can be deformed but not intrinsically changed. Topological quantum states first came to the public’s attention in 2016 when three scientists, including Duncan Haldane, who is Princeton’s Thomas D. Jones Professor of Mathematical Physics and Sherman Fairchild University Professor of Physics, were awarded the Nobel Prize for their theoretical prediction of topology in electronic materials.

May 29, 2022

DONATE: Dear all

Posted by in categories: cryptocurrencies, education, finance, mathematics, robotics/AI, space

This March, we, a group of educators, scientists, and psychologists started an educational non-profit (501 c3) Earthlings Hub, helping kids in refugee camps and evacuated orphanages. We are getting lots of requests for help, and are in urgent need to raise funds. If you happen to have any connections to educational and humanitarian charities, or if your universities or companies may be interested in providing some financial support to our program, we would really appreciate that! Please share with everyone who might be able to offer help or advice.

Our advisory board includes NASA astronaut Greg Chamitoff, Professor Uri Wilensky, early math educator Maria Droujkova, AI visionary Joscha Bach, and others.


Support Us The Earthlings Hub works with a fiscal sponsor Blue Marble Space. CREDIT CARD & PAYPAL Please contact us if you would like to via other means, such as checks, stocks, cryptocurrency, or using your Donor Advised Fund: [email protected]

May 28, 2022

Previously unnoticed mathematical property of cosmological models discovered

Posted by in category: mathematics

Ghostly ‘mirror world’ might be the cause of cosmic controversy.

May 28, 2022

Computable Artificial General Intelligence

Posted by in categories: mathematics, robotics/AI

If you are interested in artificial general intelligence (AGI), then I have a panel discussion to recommend. My friend, David Wood, has done a masterful job of selecting three panelists with deep insight into possible regulation of AGI. One of the panelists was my friend, Dan Faggella, who was eloquent and informative as usual. For this session of the London Futurists, David Wood selected two other panelists with significantly different opinions on how to properly restrain AGI.


An artificial general intelligence (AGI), by one definition, is an agent that requires less information than any other to make an accurate prediction. It is arguable that the general reinforcement learning agent AIXI not only met this definition, but was the only mathematical formalism to do so. Though a significant result, AIXI was incomputable and its performance subjective. This paper proposes an alternative formalism of AGI which overcomes both problems. Formal proof of its performance is given, along with a simple implementation and experimental results that support these claims.

May 27, 2022

Magnetic resonance imaging shows brain inflammation in vivo for the first time

Posted by in categories: biotech/medical, mathematics, neuroscience

Research by Dr. Silvia de Santis and Dr. Santiago Canals, both from the Institute of Neurosciences UMH-CSIC (Alicante, Spain), has made it possible to visualize for the first time and in great detail brain inflammation using diffusion-weighted Magnetic Resonance Imaging. This detailed “X-ray” of inflammation cannot be obtained with conventional MRI, but requires data acquisition sequences and special mathematical models. Once the method was developed, the researchers were able to quantify the alterations in the morphology of the different cell populations involved in the inflammatory process in the brain.

An innovative strategy developed by the researchers has made possible this important breakthrough, which is published today in the journal Science Advances and which may be crucial to change the course of the study and treatment of neurodegenerative diseases.

The research demonstrates that diffusion-weighted MRI can noninvasively and differentially detect the activation of microglia and astrocytes, two types of cells that are at the basis of neuroinflammation and its progression.

May 23, 2022

Topological Materials Are Everywhere — New Database Reveals Over 90,000

Posted by in categories: materials, mathematics

Searchable tool reveals more than 90,000 known materials with electronic properties that remain unperturbed in the face of disruption.

What will it take for our electronics to become smarter, faster, and more resilient? One idea is to build them out of topological materials.

Topology stems from a branch of mathematics that studies shapes that can be manipulated or deformed without losing certain essential properties. A donut is a common example: If it were made of rubber, a donut could be twisted and squeezed into a completely new shape, such as a coffee mug, while retaining a key trait — namely, its center hole, which takes the form of the cup’s handle. The hole, in this case, is a topological trait, robust against certain deformations.

May 19, 2022

Professor Sean Carroll explains the theories of Presentism and Eternalism

Posted by in categories: mathematics, physics

It’s said that the clock is always ticking, but there’s a chance that it isn’t. The theory of “presentism” states that the current moment is the only thing that’s real, while “eternalism” is the belief that all existence in time is equally real. Find out if the future is really out there and predictable—just don’t tell us who wins the big game next year.

This video is episode two from the series “Mysteries of Modern Physics: Time”, Presented by Sean Carroll.
Learn more about the physics of time at https://www.wondrium.com/YouTube.

00:00 Science and Philosophy Combine When Studying Time.
2:30 Experiments Prove Continuity of Time.
6:47 Time Is Somewhat Predictable.
8:10 Why We Think of Time Differently.
8:49 Our Perception of Time Leads to Spacetime.
11:54 We Dissect Presentism vs Eternalism.
15:43 Memories and Items From the Past Make it More Real.
17:47 Galileo Discovers Pendulum Speeds Are Identical.
25:00 Thought Experiment: “What if Time Stopped?”
29:07 Time Connects Us With the Outside World.

Continue reading “Professor Sean Carroll explains the theories of Presentism and Eternalism” »

May 17, 2022

A Power Law Keeps the Brain’s Perceptions Balanced

Posted by in categories: mathematics, robotics/AI

The human brain is often described in the language of tipping points: It toes a careful line between high and low activity, between dense and sparse networks, between order and disorder. Now, by analyzing firing patterns from a record number of neurons, researchers have uncovered yet another tipping point — this time, in the neural code, the mathematical relationship between incoming sensory information and the brain’s neural representation of that information. Their findings, published in Nature in June, suggest that the brain strikes a balance between encoding as much information as possible and responding flexibly to noise, which allows it to prioritize the most significant features of a stimulus rather than endlessly cataloging smaller details. The way it accomplishes this feat could offer fresh insights into how artificial intelligence systems might work, too.

A balancing act is not what the scientists initially set out to find. Their work began with a simpler question: Does the visual cortex represent various stimuli with many different response patterns, or does it use similar patterns over and over again? Researchers refer to the neural activity in the latter scenario as low-dimensional: The neural code associated with it would have a very limited vocabulary, but it would also be resilient to small perturbations in sensory inputs. Imagine a one-dimensional code in which a stimulus is simply represented as either good or bad. The amount of firing by individual neurons might vary with the input, but the neurons as a population would be highly correlated, their firing patterns always either increasing or decreasing together in the same overall arrangement. Even if some neurons misfired, a stimulus would most likely still get correctly labeled.

At the other extreme, high-dimensional neural activity is far less correlated. Since information can be graphed or distributed across many dimensions, not just along a few axes like “good-bad,” the system can encode far more detail about a stimulus. The trade-off is that there’s less redundancy in such a system — you can’t deduce the overall state from any individual value — which makes it easier for the system to get thrown off.

May 16, 2022

Our Reality May Only Be Half of a Pair of Interacting Worlds

Posted by in categories: mathematics, physics

Physicists sometimes come up with bizarre stories that sound like science fiction. Yet some turn out to be true, like how the curvature of space and time described by Einstein was eventually confirmed by astronomical measurements. Others linger on as mere possibilities or mathematical curiosities.

May 13, 2022

Mathematicians Coax Fluid Equations Into Nonphysical Solutions

Posted by in categories: information science, mathematics

The famed Navier-Stokes equations can lead to cases where more than one result is possible, but only in an extremely narrow set of situations.

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