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Category: mathematics – Page 135

Using data from the Hubble Space Telescope’s Cosmic Origins Spectrograph, the team was able to observe the distinctive absorption signature in the spectrum of light that passes through it, and the sight-lines of hundreds of distant quasars that pierce the volume of space occupied by the SDSS galaxies, says the university.

This lowly slime mold does a good job of characterizing the large-scale structure of the Universe over a wide range of scale, Burchett told me.

“I see how it works from a mathematical and [topological] perspective, but that doesn’t diminish my continued amazement that the slime mold-inspired method handles this difficult problem so elegantly and efficiently,” Burchett told me.

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For all of science’s impressive advancements, one problem has stubbornly eluded us: Why do we have consciousness? How does inert unconscious matter give rise to the light of conscious experience? Neuroscientist Donald Hoffman has been pondering this question throughout his career. His thinking has gradually led him to a surprising possibility — that consciousness itself is fundamental to reality. Donald’s theory, however, differs from that of the growing number of other scientists and philosophers now arriving at this conclusion.

“We’ve been stuck on the same problem for centuries. It’s time to take a different approach.”

The fundamental nature of reality, Donald theorizes, is comprised of an infinite network of interacting conscious agents. Uniquely, Donald offers a precise mathematical definition of a conscious agent. He believes the theory may be used to reconstruct the universe and existing scientific discoveries purely through the interaction of these units of consciousness.

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Circa 2002 4 lines of code to solve everything.

… But first it cracked him. The inside story of how Stephen went from boy genius to recluse to science renegade.

Word had been out that Stephen, the onetime enfant terrible of the science world, was working on a book that would Say It All, a paradigm-busting tome that would not only be the definitive account on complexity theory but also the opening gambit in a new way to view the universe. But no one had read it.

Though physically unimposing with a soft, round face and a droll English accent polished at Eton and Oxford, had already established himself as a larger-than-life figure in the gossipy world of science. A series of much-discussed reinventions made him sort of the Bob Dylan of physics. He’d been a child genius, and at 21 had been the youngest member of the storied first class of MacArthur genius awards. After laying the groundwork for a brilliant career in particle physics, he’d suddenly switched to the untraditional pursuit of studying complex systems, and, to the establishment’s dismay, dared to pioneer the use of computers as a primary research tool. Then he seemed to turn his back on that field. He started a software company to sell Mathematica, a computer language he’d written that did for higher math what the spreadsheet did for business. It made him a rich man. Now he had supposedly returned to science to write a book that would make the biggest splash of all.

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NASA announced Johnson’s death on Monday.

Johnson was part of NASA’s “Computer Pool,” a group of mathematicians whose data powered NASA’s first successful space missions. The group’s success largely hinged on the accomplishments of its black women members.

Johnson was among a group of black women mathematicians who helped power NASA’s space travel in the early 1960s when the agency was still segregated.

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Engineers at the University of Washington are working on a new type of rocket engine that holds the promise of being lighter, more efficient, and simpler to make than conventional liquid-fuel rockets. Called a Rotational Detonation Engine (RDE), one of the biggest hurdles to making it practical is to develop mathematical models that can describe how the very unpredictable engine design works in order to make it more stable.

An RDE is a rocket engine that is similar to the pulse jet engines that powered the infamous German V1 cruise missile of the Second World War, which used a simple combustion chamber with an exhaust pipe at one end and spring-mounted slats on the front face. In operation, air would come in through the slats, mix with fuel, which was then detonated, producing a pulse of thrust. An RDE takes this idea one step further.

“A rotating detonation engine takes a different approach to how it combusts propellant,” says James Koch, a UW doctoral student in aeronautics and astronautics. “It’s made of concentric cylinders. Propellant flows in the gap between the cylinders, and, after ignition, the rapid heat release forms a shock wave, a strong pulse of gas with significantly higher pressure and temperature that is moving faster than the speed of sound.

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The sophistication of autonomous systems currently being developed across various domains and industries has markedly increased in recent years, due in large part to advances in computing, modeling, sensing, and other technologies. While much of the technology that has enabled this technical revolution has moved forward expeditiously, formal safety assurances for these systems still lag behind. This is largely due to their reliance on data-driven machine learning (ML) technologies, which are inherently unpredictable and lack the necessary mathematical framework to provide guarantees on correctness. Without assurances, trust in any learning enabled cyber physical system’s (LE-CPS’s) safety and correct operation is limited, impeding their broad deployment and adoption for critical defense situations or capabilities.

To address this challenge, DARPA’s Assured Autonomy program is working to provide continual assurance of an LE-CPS’s safety and functional correctness, both at the time of its design and while operational. The program is developing mathematically verifiable approaches and tools that can be applied to different types and applications of data-driven ML algorithms in these systems to enhance their autonomy and assure they are achieving an acceptable level of safety. To help ground the research objectives, the program is prioritizing challenge problems in the defense-relevant autonomous vehicle space, specifically related to air, land, and underwater platforms.

The first phase of the Assured Autonomy program recently concluded. To assess the technologies in development, research teams integrated them into a small number of autonomous demonstration systems and evaluated each against various defense-relevant challenges. After 18 months of research and development on the assurance methods, tools, and learning enabled capabilities (LECs), the program is exhibiting early signs of progress.

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BF16, the new number format optimized for deep learning, promises power and compute savings with a minimal reduction in prediction accuracy.

BF16, sometimes called BFloat16 or Brain Float 16, is a new number format optimised for AI/deep learning applications. Invented at Google Brain, it has gained wide adoption in AI accelerators from Google, Intel, Arm and many others.

The idea behind BF16 is to reduce the compute power and energy consumption needed to multiply tensors together by reducing the precision of the numbers. A tensor is a three-dimensional matrix of numbers; multiplication of tensors is the key mathematical operation required for AI calculations.

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Circa 2017

The Middle Ages certainly were far from being science-friendly: Whoever looked for new findings off the beaten track faced the threat of being burned at the stake. Hence, the contribution of this era to technical progress is deemed to be rather small. Scientists of Karlsruhe Institute of Technology (KIT), however, were inspired by medieval mail armor when producing a new metamaterial with novel properties. They succeeded in reversing the Hall coefficient of a material.

The Hall effect is the occurrence of a transverse electric voltage across an electric conductor passed by current flow, if this conductor is located in a . This effect is a basic phenomenon of physics and allows to measure the strength of magnetic fields. It is the basis of magnetic speed sensors in cars or compasses in smartphones. Apart from measuring magnetic fields, the Hall effect can also be used to characterize metals and semiconductors and in particular to determine charge carrier density of the material. The sign of the measured Hall voltage allows conclusions to be drawn as to whether in the semiconductor element carry positive or negative charge.

Mathematicians already predicted theoretically that it is possible to reverse the Hall coefficient of a material (such as gold or silicon), i.e. to reverse its sign. This was expected to be achieved by a three-dimensional resembling medieval mail armor. How-ever, this was considered difficult, as the ring mesh of millionths of a meter in size would have to be composed of three different components.

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O.o!

A mind-expanding and funny trip to the edge of mathematics

How big is the universe? How many numbers are there? And is infinity + 1 is the same as 1 + infinity? Such questions occur to young children and our greatest minds. And they are all the same question: What is infinity? In Beyond Infinity, Eugenia Cheng takes us on a staggering journey from elemental math to its loftiest abstractions. Along the way, she considers how to use a chessboard to plan a worldwide dinner party, how to make a chicken-sandwich sandwich, and how to create infinite cookies from a finite ball of dough. Beyond Infinity shows how one little symbol holds the biggest idea of all.

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