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Category: mathematics – Page 127

AI designed to be aware of it’s own competence.

Ira Pastor, ideaXme life sciences ambassador interviews Dr. Jiangying Zhou, DARPA program manager in the Defense Sciences Office, USA.

Ira Pastor comments:

On this episode of ideaXme, we meet once more with the U.S. Defense Advanced Research Projects Agency (DARPA), but unlike the past few shows where we been spent time with thought leaders from the Biologic Technology Office (BTO), today we’re going to be focused on the Defense Sciences Office (DSO) which identifies and pursues high-risk, high-payoff research initiatives across a broad spectrum of science and engineering disciplines and transforms them into important, new game-changing technologies for U.S. national security. Current DSO themes include frontiers in math, computation and design, limits of sensing and sensors, complex social systems, and anticipating surprise.

Dr. Jiangying Zhou became a DARPA program manager in the Defense Sciences Office in November 2018, having served as a program manager in the Strategic Technology Office (STO) since January 2018. Her areas of research include machine learning, artificial intelligence, data analytics, and intelligence, surveillance and reconnaissance (ISR) exploitation technologies.

Continue reading “Expect the Unexpected: Frontiers of Mathematics, Computation, Systems and Design” | >

Sophomore math major Xzavier Herbert was never much into science fiction or the space program, but his skills in pure mathematics seem to keep drawing him into NASA’s orbit.

With an interest in representation theory, Herbert spent the summer virtually at NASA, studying connections between classical information theory and quantum information theory, each of which corresponds to a different set of laws: classical physics and quantum mechanics.

“What I’m doing involves how representation theory allows us to draw a direct analog from classical information theory to quantum information theory,” Herbert says. “It turns out that there is a mathematical way of justifying how these are related.”

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Ira Pastor, ideaXme life sciences ambassador and CEO Bioquark interviews Dr. Michelle Francl the Frank B. Mallory Professor of Chemistry, at Bryn Mawr College, and an adjunct scholar of the Vatican Observatory.

Ira Pastor comments:

Today, we have another fascinating guest working at the intersection of cutting edge science and spirituality.

Dr. Michelle Francl is the Frank B. Mallory Professor of Chemistry, at Bryn Mawr College, a distinguished women’s college in the suburbs of Philadephia, as well as an adjunct scholar of the Vatican Observatory.

Dr. Francl has a Ph.D. in chemistry from University of California, Irvine, did her post-doctoral research at Princeton University, and has taught physical chemistry, general chemistry, and mathematical modeling at Bryn Mawr College since 1986. In addition Dr. Francl has research interests in theoretical and computational chemistry, structures of topologically intriguing molecules (molecules with weird shapes), history and sociology of science, and the rhetoric of science.

Dr. Francl is noted for developing new methodologies in computational chemistry, is on a list of the 1,000 most cited chemists, is a member of the editorial board for the Journal of Molecular Graphics and Modelling, is active in the American Chemical Society, and the author of “The Survival Guide for Physical Chemistry”. In 1994, she was awarded the Christian R. and Mary F. Lindback Award by Bryn Mawr College for excellence in teaching.

Continue reading “Tripping Over the Mysteries of the Universe: Molecules, Particles and People” | >

In a story of lost and stolen books and scrupulous detective work across continents, a Caltech historian and his former student have unearthed previously uncounted copies of Isaac Newton’s groundbreaking science book Philosophiae Naturalis Principia Mathematica, known more colloquially as the Principia. The new census more than doubles the number of known copies of the famous first edition, published in 1687. The last census of this kind, published in 1953, had identified 187 copies, while the new Caltech survey finds 386 copies. Up to 200 additional copies, according to the study authors, likely still exist undocumented in public and private collections.

“We felt like Sherlock Holmes,” says Mordechai (Moti) Feingold, the Kate Van Nuys Page Professor of the History of Science and the Humanities at Caltech, who explains that he and his former student, Andrej Svorenčík (MS ‘08) of the University of Mannheim in Germany, spent more than a decade tracing copies of the book around the world. Feingold and Svorenčík are co-authors of a paper about the survey published in the journal Annals of Science.

Moreover, by analyzing ownership marks and notes scribbled in the margins of some of the books, in addition to related letters and other documents, the researchers found evidence that the Principia, once thought to be reserved for only a select group of expert mathematicians, was more widely read and comprehended than previously thought.

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A team of researchers at Samsung has developed a slim-panel holographic video display that allows for viewing from a variety of angles. In their paper published in the journal Nature Communications, the group describes their new display device and their plans for making it suitable for use with a smartphone.

Despite predictions in science-fiction books and movies over the past several decades, 3D holographic players are still not available to consumers. Existing players are too bulky and display video from limited viewing angles. In this new effort, the researchers at Samsung claim to have overcome these difficulties and built a demo device to prove it.

To build their demo device, which was approximately 25 cm tall, the team at Samsung added a steering-backlight unit with a beam deflector for increasing viewing angles. The demo had a viewing angle of 15 degrees at distances up to one meter. The beam deflector was made by sandwiching liquid crystals between sheets of glass. The end result was a device that could bend the light that came through it very much like a prism. Testing showed the beam deflector combined with a tilting mechanism increased viewing angles by 30 times compared to conventional designs. The new design also allows for a slim form at just 1 cm thick. It also has a light modulator, geometric lens and a holographic video processor capable of carrying out 140 billion operations per second. The researchers used a new algorithm that uses lookup tables rather than math operations to process the video data. The demo device was capable of displaying 4K resolution holographic video running at 30 frames per second.

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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.

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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.

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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.

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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.

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