## Archive for the ‘mathematics’ category: Page 61

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.

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

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.

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.

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.

Is neuromorphic computing the only way we can actually achieve general artificial intelligence?

Very likely yes, according to Gordon Wilson, CEO of Rain Neuromorphics, who is trying to recreate the human brain in hardware and “give machines all of the capabilities that we recognize in ourselves.”

A new computer program fashioned after artificial intelligence systems like AlphaGo has solved several open problems in combinatorics and graph theory.

A new review paper on magnetic topological materials introduces a theoretical concept that interweaves magnetism and topology. It identifies and surveys potential new magnetic topological materials and suggests possible future applications in spin and quantum electronics and as materials for efficient energy conversion.

Magnetic topological materials represent a class of compounds whose properties are strongly influenced by the of the electronic wavefunctions coupled with their spin configuration. Topology is a simple concept dealing with the surfaces of objects. The topology of a mathematical structure is identical if it is preserved under continuous deformation. A pancake has the same topology as a cube, a donut as a coffee cup, and a pretzel as a board with three holes. Adding spin offers additional structure—a new degree of freedom—for the realization of new states of matter that are not known in non-magnetic materials. Magnetic topological materials can support chiral channels of electrons and spins, and can be used for an array of applications including information storage, control of dissipationless spin and charge transport, and giant responses under such as temperature and light.

The review summarizes the theoretical and experimental progress achieved in the field of magnetic topological materials beginning with the theoretical prediction of the quantum anomalous Hall effect without Landau levels, leading to recent discoveries of magnetic Weyl semimetals and antiferromagnetic topological insulators. It also outlines recent tabulations of all magnetic symmetry group representations and topology. As a result, all known magnetic materials—including future discoveries—can be fully characterized by their topological properties. The identification of materials for a specific technological application (e.g., quantum anomalous Hall) is straightforward.

In a vacuum like space, the speed of light is just over 186,280 miles per second. Scientists have now shown it’s possible to slow it down to zero miles per second without sacrificing its brightness, regardless of its frequency or bandwidth.

A team of researchers from the Israel Institute of Technology and the Institute of Pure and Applied Mathematics in Brazil discovered a method of theoretically bringing the speed of light to a halt by capitalizing on “exceptional points”—coordinates at which two separate light emissions reach each other and merge into a single one, according to Phys.org. A paper describing the research was published in the scientific journal Physical Review Letters.

A huge amount of mysterious dark energy is necessary to explain cosmological phenomena, such as the accelerated expansion of the Universe, using Einstein’s theory. But what if dark energy was just an illusion and general relativity itself had to be modified? A new SISSA study, published in Physical Review Letters, offers a new approach to answer this question. Thanks to huge computational and mathematical effort, scientists produced the first simulation ever of merging binary neutron stars in theories beyond general relativity that reproduce a dark-energy like behavior on cosmological scales. This allows the comparison of Einstein’s theory and modified versions of it, and, with sufficiently accurate data, may solve the dark energy mystery.

For about 100 years now, general relativity has been very successful at describing gravity on a variety of regimes, passing all experimental tests on Earth and the solar system. However, to explain cosmological observations such as the observed accelerated expansion of the Universe, we need to introduce dark components, such as and , which still remain a mystery.

Enrico Barausse, astrophysicist at SISSA (Scuola Internazionale Superiore di Studi Avanzati) and principal investigator of the ERC grant GRAMS (GRavity from Astrophysical to Microscopic Scales) questions whether dark is real or, instead, it may be interpreted as a breakdown of our understanding of gravity. “The existence of dark energy could be just an illusion,” he says, “the accelerated expansion of the Universe might be caused by some yet unknown modifications of general relativity, a sort of ‘dark gravity’.”

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