## Archive for the ‘mathematics’ category: Page 104

Unless you’re a physicist or an engineer, there really isn’t much reason for you to know about partial differential equations. I know. After years of poring over them in undergrad while studying mechanical engineering, I’ve never used them since in the real world.

But partial differential equations, or PDEs, are also kind of magical. They’re a category of math equations that are really good at describing change over space and time, and thus very handy for describing the physical phenomena in our universe. They can be used to model everything from planetary orbits to plate tectonics to the air turbulence that disturbs a flight, which in turn allows us to do practical things like predict seismic activity and design safe planes.

The catch is PDEs are notoriously hard to solve. And here, the meaning of “solve” is perhaps best illustrated by an example. Say you are trying to simulate air turbulence to test a new plane design. There is a known PDE called Navier-Stokes that is used to describe the motion of any fluid. “Solving” Navier-Stokes allows you to take a snapshot of the air’s motion (a.k.a. wind conditions) at any point in time and model how it will continue to move, or how it was moving before.

Tuomas Sandholm, a computer scientist at Carnegie Mellon University, is not a poker player—or much of a poker fan, in fact—but he is fascinated by the game for much the same reason as the great game theorist John von Neumann before him. Von Neumann, who died in 1957, viewed poker as the perfect model for human decision making, for finding the balance between skill and chance that accompanies our every choice. He saw poker as the ultimate strategic challenge, combining as it does not just the mathematical elements of a game like chess but the uniquely human, psychological angles that are more difficult to model precisely—a view shared years later by Sandholm in his research with artificial intelligence.

“Poker is the main benchmark and challenge program for games of imperfect information,” Sandholm told me on a warm spring afternoon in 2018, when we met in his offices in Pittsburgh. The game, it turns out, has become the gold standard for developing artificial intelligence.

Tall and thin, with wire-frame glasses and neat brow hair framing a friendly face, Sandholm is behind the creation of three computer programs designed to test their mettle against human poker players: Claudico, Libratus, and most recently, Pluribus. (When we met, Libratus was still a toddler and Pluribus didn’t yet exist.) The goal isn’t to solve poker, as such, but to create algorithms whose decision making prowess in poker’s world of imperfect information and stochastic situations—situations that are randomly determined and unable to be predicted—can then be applied to other stochastic realms, like the military, business, government, cybersecurity, even health care.

Ivan Smirnov, Leading Research Fellow of the Laboratory of Computational Social Sciences at the Institute of Education of HSE University, has created a computer model that can distinguish high academic achievers from lower ones based on their social media posts. The prediction model uses a mathematical textual analysis that registers users’ vocabulary (its range and the semantic fields from which concepts are taken), characters and symbols, post length, and word length.

Every word has its own rating (a kind of IQ). Scientific and cultural topics, English words, and words and posts that are longer in length rank highly and serve as indicators of good academic performance. An abundance of emojis, words or whole phrases written in capital letters, and vocabulary related to horoscopes, driving, and military service indicate lower grades in school. At the same time, posts can be quite short—even tweets are quite informative. The study was supported by a grant from the Russian Science Foundation (RSF), and an article detailing the study’s results was published in EPJ Data Science.

Foreign studies have long shown that users’ social media behavior—their posts, comments, likes, profile features, user pics, and photos—can be used to paint a comprehensive portrait of them. A person’s social media behavior can be analyzed to determine their lifestyle, personal qualities, individual characteristics, and even their mental health status. It is also very easy to determine a person’s socio-demographic characteristics, including their age, gender, race, and income. This is where profile pictures, Twitter hashtags, and Facebook posts come in.

A pair of statisticians at the University of Waterloo has proposed a math process idea that might allow for teaching AI systems without the need for a large dataset. Ilia Sucholutsky and Matthias Schonlau have written a paper describing their idea and published it on the arXiv preprint server.

Artificial intelligence (AI) applications have been the subject of much research lately, with the development of , researchers in a wide range of fields began finding uses for it, including creating deepfake videos, board game applications and medical diagnostics.

Deep learning networks require large datasets in order to detect patterns revealing how to perform a given task, such as picking a certain face out of a crowd. In this new effort, the researchers wondered if there might be a way to reduce the size of the dataset. They noted that children only need to see a couple of pictures of an animal to recognize other examples. Being statisticians, they wondered if there might be a way to use mathematics to solve the problem.

Black holes are perhaps the most mysterious objects in nature. They warp space and time in extreme ways and contain a mathematical impossibility, a singularity – an infinitely hot and dense object within. But if black holes exist and are truly black, how exactly would we ever be able to make an observation?

This morning the Nobel Committee announced that the 2020 Nobel Prize in physics will be awarded to three scientists – Sir Roger Penrose, Reinhard Genzel and Andrea Ghez – who helped discover the answers to such profound questions. Andrea Ghez is only the fourth woman to win the Nobel Prize in physics.

A team of researchers affiliated with a host of institutions in Korea and one in Estonia has found a way to use math to study paintings to learn more about the evolution of art history in the western world. In their paper published in Proceedings of the National Academy of Sciences, the group describes how they scanned thousands of paintings and then used mathematical algorithms to find commonalities between them over time.

Beauty, as the saying goes, is in the eye of the beholder—and so it is also with art. Two people looking at the same can walk away with vastly different impressions. But art also serves, the researchers contend, as a barometer for visualizing the emotional tone of a given society. This suggests that the study of art history can serve as a channel of sorts—illuminating societal trends over time. The researchers further note that to date, most studies of art history have been qualitatively based, which has led to interpretive results. To overcome such bias, the researchers with this new effort looked to mathematics to see if it might be useful in uncovering features of paintings that have been overlooked by human scholars.

The work involved digitally scanning 14,912 paintings—all of which (except for two) were painted by Western artists. The data for each of the paintings was then sent through a mathematical that drew partitions on the based on contrasting colors. The researchers ran the algorithm on each painting multiple times, each time creating more partitions. As an example, the first run of the algorithm might have simply created two partitions on a painting—everything on land, and everything in the sky. The second might have split the land into buildings in one partition and farmland in another.

Have you ever been in more than one place at the same time? If you’re much bigger than an atom, the answer will be no.

But atoms and particles are governed by the rules of quantum mechanics, in which several different possible situations can coexist at once.

The ‘Universal law of touch’ theory was created by researchers at the University of Birmingham, who used mathematical modelling of touch receptors in humans and other animal species. By applying the mathematics of earthquakes to model how vibrations travel through the skin, the team discovered that vibration receptors beneath the skin respond to Rayleigh waves in the same way regardless of age, gender, or even species.

Breakthrough appears to support Elon Musk’s claim we are living in a simulation.

DALLAS, Sept. 29, 2020 /PRNewswire/ — The National Math and Science Initiative has named veteran fundraiser Laure O’Neal as its first chief development officer, charging her and a restructured fundraising team with diversifying the organization’s funding sources.

NMSI was founded in 2007 with generous support from the ExxonMobil Foundation, Texas Instruments Foundation and other corporate and philanthropic organizations. It continues to receive financial support from those and other organizations and is expanding its fundraising to more quickly reach additional students, teachers and school systems across the country.

“Laure brings two decades of experience in connecting corporate, foundation and individual givers with academic institutions and other organizations that support individuals and communities,” said NMSI CEO Bernard A. Harris, Jr. “I’m excited about the energy and expertise Laure brings to secure new support to reach more communities with our programs.”

A new study proves that far from being mere mathematical artifacts, particles that are indistinguishable from one another can be a potent resource in real-world experiments.