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Archive for the ‘mathematics’ category: Page 86

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.

May 11, 2022

Bilayer graphene inspires two-universe cosmological model

Posted by in categories: mathematics, quantum physics

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

In a new paper in Physical Review Research, JQI Fellow Victor Galitski and JQI graduate student Alireza Parhizkar have explored the imaginative possibility that our reality is only one half of a pair of interacting worlds. Their may provide a new perspective for looking at fundamental features of reality—including why our universe expands the way it does and how that relates to the most miniscule lengths allowed in quantum mechanics. These topics are crucial to understanding our universe and are part of one of the great mysteries of modern .

The pair of scientists stumbled upon this new perspective when they were looking into research on sheets of graphene—single atomic layers of carbon in a repeating . They realized that experiments on the electrical properties of stacked sheets of graphene produced results that looked like little universes and that the underlying phenomenon might generalize to other areas of physics. In stacks of graphene, new electrical behaviors arise from interactions between the individual sheets, so maybe unique physics could similarly emerge from interacting layers elsewhere—perhaps in cosmological theories about the entire universe.

May 7, 2022

In Fake Universes, Evidence for String Theory

Posted by in categories: mathematics, quantum physics, space

Circa 2015 o.o!


The publication of Green and Schwarz’s paper “was 30 years ago this month,” the string theorist and popular-science author Brian Greene wrote in Smithsonian Magazine in January, “making the moment ripe for taking stock: Is string theory revealing reality’s deep laws? Or, as some detractors have claimed, is it a mathematical mirage that has sidetracked a generation of physicists?” Greene had no answer, expressing doubt that string theory will “confront data” in his lifetime.

Recently, however, some string theorists have started developing a new tactic that gives them hope of someday answering these questions. Lacking traditional tests, they are seeking validation of string theory by a different route. Using a strange mathematical dictionary that translates between laws of gravity and those of quantum mechanics, the researchers have identified properties called “consistency conditions” that they say any theory combining quantum mechanics and gravity must meet. And in certain highly simplified imaginary worlds, they claim to have found evidence that the only consistent theories of “quantum gravity” involve strings.

Continue reading “In Fake Universes, Evidence for String Theory” »

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