Archive for the ‘mathematics’ category: Page 40

Mar 15, 2022

Mathematical discovery could shed light on quantum gravity

Posted by in categories: cosmology, mathematics, quantum physics

How can Einstein’s theory of gravity be unified with quantum mechanics? It is a challenge that could give us deep insights into phenomena such as black holes and the birth of the universe. Now, a new article in Nature Communications, written by researchers from Chalmers University of Technology, Sweden, and MIT, U.S., presents results that cast new light on important challenges in understanding quantum gravity.

A grand challenge in modern theoretical physics is to find a “unified theory” that can describe all the laws of nature within a single framework—connecting Einstein’s general theory of relativity, which describes the universe on a large scale, and quantum mechanics, which describes our world at the . Such a theory of “” would include both a macroscopic and microscopic description of nature.

“We strive to understand the laws of nature and the language in which these are written is mathematics. When we seek answers to questions in physics, we are often led to new discoveries in mathematics too. This interaction is particularly prominent in the search for quantum gravity—where it is extremely difficult to perform experiments,” explains Daniel Persson, Professor at the Department of Mathematical Sciences at Chalmers university of technology.

Mar 14, 2022

Study highlights the potential of neuromorphic architectures to perform random walk computations

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

Over the past decade or so, many researchers worldwide have been trying to develop brain-inspired computer systems, also known as neuromorphic computing tools. The majority of these systems are currently used to run deep learning algorithms and other artificial intelligence (AI) tools.

Researchers at Sandia National Laboratories have recently conducted a study assessing the potential of neuromorphic architectures to perform a different type of computations, namely random walk computations. These are computations that involve a succession of random steps in the mathematical space. The team’s findings, published in Nature Electronics, suggest that neuromorphic architectures could be well-suited for implementing these computations and could thus reach beyond machine learning applications.

“Most past studies related to focused on cognitive applications, such as ,” James Bradley Aimone, one of the researchers who carried out the study, told TechXplore. “While we are also excited about that direction, we wanted to ask a different and complementary question: can neuromorphic computing excel at complex math tasks that our brains cannot really tackle?”

Mar 14, 2022

Wormholes — Shortcuts Connecting Two Points in Spacetime — Help Resolve Black Hole Information Paradox

Posted by in categories: cosmology, mathematics, quantum physics

A mathematical analysis helps illuminate the puzzle over how information escapes from a black hole.

A RIKEN physicist and two colleagues have found that a wormhole—a bridge connecting distant regions of the Universe—helps to shed light on the mystery of what happens to information about matter consumed by black holes.

Einstein’s theory of general relativity predicts that nothing that falls into a black hole can escape its clutches. But in the 1970s, Stephen Hawking calculated that black holes should emit radiation when quantum mechanics, the theory governing the microscopic realm, is considered. “This is called black hole evaporation because the black hole shrinks, just like an evaporating water droplet,” explains Kanato Goto of the RIKEN Interdisciplinary Theoretical and Mathematical Sciences.

Mar 13, 2022

This Month in Physics History

Posted by in categories: mathematics, particle physics, quantum physics

Many people say that Einstein failed because he was simply ahead of his time. The knowledge and tools needed to complete a unified theory simply hadn’t been developed before Einstein died in 1955.

Today, many physicists are taking up his quest. The most promising approach appears to be string theory, which requires 10 or more dimensions and describes all elementary particles as vibrating strings, with different modes of vibration producing different particles.

String theory has not yet made any testable predictions, and some scientists worry that string theorists have, like Einstein in his later years, strayed too far from physical reality in their obsession with beautiful mathematics. But many others believe string theory does indeed hold the key to completing Einstein’s quest, and researchers are hoping to find ways to test some of the predictions of string theory.

Mar 12, 2022

Faster analog computer could be based on mathematics of complex systems

Posted by in categories: mathematics, quantum physics, supercomputing

Researchers have proposed a novel principle for a unique kind of computer that would use analog technology in place of digital or quantum components.

The unique device would be able to carry out complex computations extremely quickly—possibly, even faster than today’s supercomputers and at vastly less cost than any existing quantum computers.

The principle uses to overcome the barriers in optimization problems (choosing the best option from a large number of possibilities), such as Google searches—which aim to find the optimal results matching the search request.

Mar 12, 2022

Researchers develop hybrid human-machine framework for building smarter AI

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

From chatbots that answer tax questions to algorithms that drive autonomous vehicles and dish out medical diagnoses, artificial intelligence undergirds many aspects of daily life. Creating smarter, more accurate systems requires a hybrid human-machine approach, according to researchers at the University of California, Irvine. In a study published this month in Proceedings of the National Academy of Sciences, they present a new mathematical model that can improve performance by combining human and algorithmic predictions and confidence scores.

“Humans and machine algorithms have complementary strengths and weaknesses. Each uses different sources of information and strategies to make predictions and decisions,” said co-author Mark Steyvers, UCI professor of cognitive sciences. “We show through empirical demonstrations as well as theoretical analyses that humans can improve the predictions of AI even when human accuracy is somewhat below [that of] the AI—and vice versa. And this accuracy is higher than combining predictions from two individuals or two AI algorithms.”

To test the framework, researchers conducted an image classification experiment in which human participants and computer algorithms worked separately to correctly identify distorted pictures of animals and everyday items—chairs, bottles, bicycles, trucks. The human participants ranked their confidence in the accuracy of each image identification as low, medium or high, while the machine classifier generated a continuous score. The results showed large differences in confidence between humans and AI algorithms across images.

Mar 11, 2022

Math’s ‘Oldest Problem Ever’ Gets a New Answer

Posted by in category: mathematics

A new proof significantly strengthens a decades-old result about the ubiquity of ways to represent whole numbers as sums of unit fractions.

Mar 11, 2022

A DNA “Oracle” for Predicting the Future Evolution of Gene Regulation

Posted by in categories: biotech/medical, evolution, genetics, mathematics

Researchers created a mathematical framework to examine the genome and detect signatures of natural selection, deciphering the evolutionary past and future of non-coding DNA.

Despite the sheer number of genes that each human cell contains, these so-called “coding” DNA sequences comprise just 1% of our entire genome. The remaining 99% is made up of “non-coding” DNA — which, unlike coding DNA, does not carry the instructions to build proteins.

One vital function of this non-coding DNA, also called “regulatory” DNA, is to help turn genes on and off, controlling how much (if any) of a protein is made. Over time, as cells replicate their DNA to grow and divide, mutations often crop up in these non-coding regions — sometimes tweaking their function and changing the way they control gene expression. Many of these mutations are trivial, and some are even beneficial. Occasionally, though, they can be associated with increased risk of common diseases, such as type 2 diabetes, or more life-threatening ones, including cancer.

Mar 11, 2022

Wormholes Could Help Solve an Infamous Black Hole Paradox, Says Fun New Paper

Posted by in categories: cosmology, mathematics, quantum physics

What happens to information after it has passed beyond the event horizon of a black hole? There have been suggestions that the geometry of wormholes might help us solve this vexing problem – but the math has been tricky, to say the least.

In a new paper, an international team of physicists has found a workaround for better understanding how a collapsing black hole can avoid breaking the fundamental laws of quantum physics (more on that in a bit).

Although highly theoretical, the work suggests there are likely things we are missing in the quest to resolve general relativity with quantum mechanics.

Mar 11, 2022

The Simplest Math Problem No One Can Solve

Posted by in category: mathematics

Multiply an odd number by an odd number and then add 1 always gives an even number.

Divide an even number by 2 gives an odd number half of the time and an even number half of the time.

Therefore these formulae leans towards even numbers as the output and hence if you do the calculation enough times, you will eventually end up in the 4−2−1 loop.

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